HSN.VM.C.9Common CoreMathNumber and QuantityGrades 9-12
HSN.VM.C.9: Properties of Matrix Multiplication
In plain English: HSN.VM.C.9 is an advanced (+) Common Core number and quantity standard, usually taught in Precalculus. Students show that, unlike multiplication of numbers, multiplying square matrices is not commutative: AB and BA are often different. They also show that it still satisfies the associative property, (AB)C = A(BC), and the distributive properties A(B + C) = AB + AC and (A + B)C = AC + BC.
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
Common Core State Standards for Mathematics · Domain: Vector and Matrix Quantities (VM) · Cluster: Perform operations on matrices and use matrices in applications. Also written as HSN-VM.C.9 or N-VM.9 · Official standard
Students compare the properties of matrix multiplication with the properties of multiplying real numbers. For numbers, ab = ba always. For square matrices of the same size, AB and BA are both defined and have the same size, but they are often different, so matrix multiplication is not commutative. It does keep two familiar properties: it is associative, (AB)C = A(BC), and it distributes over addition from both sides, A(B + C) = AB + AC and (A + B)C = AC + BC.
Students test each property with their own computations, find a pair of matrices that do not commute and a pair that happen to commute, and see what the missing commutative property changes in algebra: (A + B)² is A² + AB + BA + B², which is not A² + 2AB + B² unless AB = BA. Matrices on this page are written row by row, with rows separated by semicolons: [1 2; 0 1] has first row 1, 2 and second row 0, 1.
Learning Objectives
By the end of this lesson, students will be able to:
Show with a counterexample that AB and BA can differ for square matrices, and explain why one commuting pair does not make matrix multiplication commutative
Verify the associative property (AB)C = A(BC) for 2 × 2 matrices and explain why ABC can be written without parentheses
Verify both distributive properties, A(B + C) = AB + AC and (A + B)C = AC + BC, keeping each factor on its own side
Expand matrix expressions such as (A + B)² and (A - B)(A + B) correctly, and explain when the number shortcuts fail
Prior Knowledge Required
Students should already be comfortable with:
Adding and multiplying matrices of appropriate dimensions HSN.VM.C.8
The commutative, associative and distributive properties of real numbers 6.EE.A.3
Expanding products of polynomials such as (x + y)² HSA.APR.A.1
Finding a counterexample to show that a general statement is false
"(1) Is 4 · 7 = 7 · 4? Is 9 - 2 = 2 - 9? Is (2 · 3) · 5 = 2 · (3 · 5)? Name the property each question tests. (2) Compute [1 1; 0 1][2 0; 0 1] and then [2 0; 0 1][1 1; 0 1]. Did switching the order change the answer?"
For (1), students name the commutative property of multiplication (true), notice that subtraction is not commutative, and name the associative property (true). For (2), the products are [2 1; 0 1] and [2 2; 0 1]. Record both on the board and ask whether multiplication of matrices behaves like multiplication of numbers. Leave the question open: the lesson tests each property in turn.
Direct Instruction20 minutes
Part 1: Not commutative. A general property must hold for every choice of matrices, so one counterexample is enough to show that it fails. Use Diagram 1 with the first example below, then show the second example: some pairs do commute, which is why the standard says the operation is not commutative, not that AB never equals BA.
Part 2: Associative and distributive. These properties hold for all square matrices of the same size. Give students the three statements and a procedure for testing any of them:
Write the property: associative (AB)C = A(BC); left distributive A(B + C) = AB + AC; right distributive (A + B)C = AC + BC.
Compute the left side exactly as grouped: work inside the parentheses first.
Compute the right side the same way, keeping every factor in its original position from left to right.
Compare entry by entry: equal matrices must match in every position.
Draw the right conclusion: a match for one example supports a property but does not prove it; a mismatch proves that a statement is not a property.
A pair that does not commute
Let A = [1 2; 0 1] and B = [1 0; 3 1]. Compute AB and BA.
Equation: AB = [7 2; 3 1] but BA = [1 2; 3 7], so AB ≠ BA
A pair that happens to commute
Let A = [2 1; 0 2] and B = [3 4; 0 3]. Compute AB and BA.
Equation: AB = BA = [6 11; 0 6]
Associative property
Let A = [1 -1; 2 0], B = [0 1; 1 1] and C = [2 0; 1 3]. Compute (AB)C and A(BC).
Equation: AB = [-1 0; 0 2] and BC = [1 3; 3 3]; both groupings give [-2 0; 2 6]
Distributive property
Let A = [2 1; -1 3], B = [1 0; 2 -1] and C = [0 4; 1 1]. Compare A(B + C) with AB + AC.
Equation: A(B + C) = A[1 4; 3 0] = [5 8; 8 -4], and AB + AC = [4 -1; 5 -3] + [1 9; 3 -1] = [5 8; 8 -4]
What the missing property changes
Expand (A + B)² for the matrices of the first example, and compare it with A² + 2AB + B².
Equation: (A + B)² = A² + AB + BA + B² = [10 8; 12 10], but A² + 2AB + B² = [16 8; 12 4]
Use Diagram 2 to stress what associativity does and does not allow: the grouping can change, but the order A, B, C cannot. For the last example, show the expansion with the distributive property: (A + B)(A + B) = A(A + B) + B(A + B) = A² + AB + BA + B². The middle terms AB and BA can be combined into 2AB only when they are equal. Compare with polynomials, where xy = yx makes the shortcut work (HSA.APR.A.1).
Guided Practice15 minutes
Pairs work with A = [0 1; 1 0], B = [1 2; 3 4] and C = [1 -1; 0 2]. (1) Compute AB and BA and describe what A does to the rows or columns of B in each order. (Answer: AB = [3 4; 1 2] swaps the rows of B; BA = [2 1; 4 3] swaps its columns.) (2) Check the right distributive property: compute (A + B)C, then AC + BC. (Both are [1 5; 4 4].) (3) A student writes (A + B)C = CA + CB. Test the student's version with these matrices and explain the error. Listen for students who reverse factors while distributing, and for students who conclude from one matching example that a statement is always true.
Independent Practice15 minutes
Students work alone with P = [2 0; 1 -1], Q = [1 3; 2 0] and R = [1 1; -1 0]: (1) compute PQ and QP (answers: [2 6; -1 3] and [5 -3; 4 0]); (2) verify that (PQ)R = P(QR) (both [-4 2; -4 -1]); (3) compute (P - Q)(P + Q) and P² - Q² and use the distributive property to explain why they differ (answers: [-6 6; -6 -2] and [-3 -3; -1 -5]); (4) in one or two sentences, explain why matching results for one set of matrices do not prove a property, while one mismatch disproves a statement.
Closure5-10 minutes
Exit ticket: (1) A classmate cancels a step "AB - BA = 0" in an expansion. Is that step safe? Why or why not? (No: it is true only for matrices that commute.) (2) True or false: A(BC) = (AB)C for all 2 × 2 matrices A, B and C. (True, the associative property.) (3) Use the distributive property to expand A(B + C)D without changing the order of any factors. (ABD + ACD.)
Differentiation Strategies
For Struggling Students
Give a two-column template, "left side" and "right side", so students compute each side of a property separately before comparing entries
Let students use a matrix calculator for the arithmetic once they have done one product by hand, so the focus stays on comparing results
Post the three properties with the factors color-coded, so A stays in the same color and the same position on both sides
For Advanced Students
Ask students to prove that A(B + C) = AB + AC for all 2 × 2 matrices by writing A, B and C with letter entries and comparing one entry of each side
Ask students to describe every matrix of the form [a b; 0 a] and explain why any two of them commute
Ask students to show that (AB)C = A(BC) for 2 × 2 matrices by comparing the entry in row 1, column 1 of both sides with letter entries
Assessment Guidance
What to Look For
Check that students can give a specific counterexample for commutativity and say why one example is enough to disprove a general property but not enough to prove one. When they verify associative or distributive properties, look for work on both sides with the factors kept in order, and for an entry-by-entry comparison. In expansions, look for AB and BA written as separate terms. A student who writes 2AB for AB + BA, or who distributes A(B + C) as BA + CA, is still treating matrices as if they commute.
02
Classroom Activities
3 Activities
1
The Swap Test
15 minGroups of 4
Each group member takes one card with a pair of 2 × 2 matrices, computes both orders of the product and reports to the group. The group then looks for what the commuting pairs have in common.
The 4 Cards
Card 1: [2 1; 1 1] and [1 -1; 0 1]
Card 2: [3 0; 0 3] and [5 -2; 1 4]
Card 3: [1 2; 0 3] and [0 1; 1 0]
Card 4: [1 2; 2 1] and [3 1; 1 3]
Procedure
For your card, compute the first matrix times the second and the second times the first
Record both products on a class chart and mark the card "commute" or "do not commute"
Two cards commute and two do not. Is matrix multiplication commutative? What would you need to show it is?
On Card 2, the first matrix multiplies every entry of the second by 3. Why does that make the order not matter?
Write a new pair of 2 × 2 matrices that you predict will not commute, then test your prediction
2
Always or Only Sometimes?
20 minPairs
Pairs sort 8 statement cards about 2 × 2 matrices into "always true" and "only sometimes true". Every "sometimes" card needs a counterexample, and every "always" card needs at least one computed example and the name of the property.
The 8 Statement Cards
AB = BA
(AB)C = A(BC)
A(B + C) = AB + AC
(A + B)C = AC + BC
A + B = B + A
A(B + C) = BA + CA
(A + B)² = A² + 2AB + B²
(AB)² = A²B²
Procedure
Sort the cards first by prediction, then test each one with matrices of your choice
Key: always true are (AB)C = A(BC), both distributive statements, and A + B = B + A. Only sometimes true are AB = BA, A(B + C) = BA + CA, (AB)² = A²B², and (A + B)² = A² + 2AB + B², which holds exactly when AB = BA
For the (A + B)² card, find one pair where it holds and one where it fails
Discussion Questions
Matrix addition is commutative, but matrix multiplication is not. Why does the definition of addition make the order not matter?
Which "sometimes" cards become "always" if you add the condition AB = BA?
3
Two Routes to the Snack Order Totals
15 minGroups of 3
Groups use three matrices from a snack order to see the associative property in context: two different groupings answer the same question, and one of them takes less work.
The Data
Q: two stores order small and large snack boxes. Q = [10 4; 6 8] (rows: Store 1, Store 2; columns: small, large)
B: what is inside each box. B = [6 2; 12 6] (rows: small, large; columns: granola bars, trail mix bags)
C: cost and weight of each snack. C = [0.5 45; 1.2 120] (rows: bar, bag; columns: cost in dollars, weight in grams)
Procedure
Route 1: compute QB (snacks per store), then (QB)C (key: QB = [108 44; 132 60])
Route 2: compute BC (cost and weight per box), then Q(BC) (key: BC = [5.4 510; 13.2 1260])
Compare: both routes give [106.8 10140; 138 13140], the total cost in dollars and total weight in grams for each store
Discussion Questions
What does each intermediate matrix, QB and BC, mean in the context?
If the stores change their orders every week but the boxes stay the same, which route saves work, and why?
Could you compute (QC)B instead? Explain in terms of both the meaning and the commutative property.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: AB and BA Are Different Products
The products AB and BA of A = [1 2; 0 1] and B = [1 0; 3 1] share two entries but differ in the other two (shown in red), so AB ≠ BA. One such pair is enough to show that matrix multiplication is not commutative.
Diagram 2: The Associative Property
Computing AB first and then multiplying by C gives the same matrix as computing BC first and then multiplying A by it. The grouping changes, but the order of the factors does not.
04
Homework Assignment
~30 min
HSN.VM.C.9 Homework: Properties of Matrix Multiplication
Directions: Show every matrix product you compute, and compare results entry by entry. When you decide whether a statement is always true, name the property or give a counterexample.
Part 1: Order Matters (Problems 1-2)
Let A = [3 1; -2 0] and B = [1 4; 2 -1]. Compute AB and BA. What do your results show about matrix multiplication?
Let A = [1 2; 0 3] and B = [4 k; 0 6]. Find every value of k for which AB = BA. Then explain why finding such a value does not make matrix multiplication commutative.
Part 2: Associative and Distributive Properties (Problems 3-4)
Let A = [1 0; 2 -1], B = [3 1; 1 0] and C = [0 2; -1 1]. Compute AB, then (AB)C. Compute BC, then A(BC). Which property do your results illustrate?
Let A = [2 -1; 0 1], B = [1 1; 3 0] and C = [-2 0; 1 4]. (a) Show that A(B + C) = AB + AC. (b) Show that (B + C)A = BA + CA. (c) Is AB + AC equal to BA + CA for these matrices? Explain why that does not contradict parts (a) and (b).
Part 3: Reasoning with the Properties (Problems 5-6)
Use the distributive property to expand (A + 2B)² and (A + B)(A - B) for square matrices A and B, without assuming AB = BA. Then test both expansions, and the number shortcuts A² + 4AB + 4B² and A² - B², with A = [0 1; 0 0] and B = [0 0; 1 0].
A bakery supplies two cafes. Q = [2 3; 4 1] gives the daily order (rows: Cafe A, Cafe B; columns: cakes, pies). R = [3 4; 2 1] gives the ingredients per item (rows: cake, pie; columns: cups of flour, eggs). C = [0.25; 0.40] gives the cost in dollars of a cup of flour and of an egg. (a) Compute RC and say what it means. (b) Find each cafe's daily ingredient cost two ways, as Q(RC) and as (QR)C. (c) Which property explains why the answers agree?
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Products
All products computed correctly with factors in the right order
One or two arithmetic errors
Several errors or factors reversed
Commutativity
Counterexample shown and explained; k found and interpreted
Correct products, conclusion missing
Claims AB = BA in general
Associative and Distributive
Both sides computed and compared; properties named
One side or one property missing
Properties not tested
Expansions and Context
AB and BA kept separate; context results explained
Expansion or explanation incomplete
Uses 2AB or A² - B² without justification
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again. Matrices are written row by row, with rows separated by semicolons, and A, B, C and D stand for square matrices of the same size.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which property of multiplying real numbers does NOT hold in general for multiplying square matrices?
Answer: B
Matrix multiplication of square matrices is not commutative: for many pairs, AB ≠ BA. The associative and distributive properties do hold, which is exactly what the standard asks students to understand. Choice D is also true for square matrices, so it is not the answer.
Question 2 of 20 · Multiple Choice
Let A = [1 0; 2 1] and B = [0 1; 1 0]. Compute BA.
Answer: B
Row 1 of B times the columns of A: 0(1) + 1(2) = 2 and 0(0) + 1(1) = 1. Row 2: 1(1) + 0(2) = 1 and 1(0) + 0(1) = 0. So BA = [2 1; 1 0]. Choice A is AB, the product in the other order. Choice C multiplies matching entries, and choice D adds the matrices.
Question 3 of 20 · Multiple Choice
Use the matrices from question 2, A = [1 0; 2 1] and B = [0 1; 1 0]. Which statement is true?
Answer: A
AB = [0 1; 1 2] and BA = [2 1; 1 0], so AB ≠ BA and this pair shows that the commutative property fails. Choice D goes too far: some pairs do commute, so the correct statement is that multiplication is not commutative in general, not that AB never equals BA.
Question 4 of 20 · Multiple Choice
For all 2 × 2 matrices P, Q and R, which equation is always true?
Answer: C
The associative property holds for all square matrices of the same size. Choice A is the commutative property, which fails. Choice B distributes P on the wrong side. Choice D assumes PQ = QP to combine PQ + QP into 2PQ.
Question 5 of 20 · Multiple Choice
Which expression is always equal to (P + Q)R?
Answer: A
This is the right distributive property: R stays on the right of each term, so (P + Q)R = PR + QR. Choices B and D put R on the left, which is a different product unless the matrices commute. Choice C mixes the two sides.
Question 6 of 20 · Multiple Choice
Use the distributive property to expand (A + B)(C + D) for square matrices.
Answer: C
Distribute (A + B) over C + D: (A + B)C + (A + B)D = AC + BC + AD + BD, keeping each left factor on the left. Choice A drops the cross terms, a common error from treating the product like a sum of matching parts. Choice B reverses every product, and choice D reverses two of them.
Question 7 of 20 · Multiple Choice
A student finds two 2 × 2 matrices with AB = BA and concludes that matrix multiplication is commutative. What is the best response?
Answer: D
A property must hold for all matrices. A single commuting pair is allowed, but one pair with AB ≠ BA, such as A = [1 2; 0 1] and B = [1 0; 3 1] from the lesson examples, shows that the commutative property does not hold in general. Choice B is too strong, because some pairs do commute.
Question 8 of 20 · Multiple Choice
Which pair of matrices commutes, that is, has AB = BA?
Answer: A
For choice A, both products equal [1 4; 0 1]. For each of the other pairs, computing both orders gives two different matrices; for example, in choice C the products are [0 2; 1 0] and [0 1; 2 0]. Students should compute both orders rather than guess from the entries.
Question 9 of 20 · Multiple Choice
You know that A = [1 1; 0 1] and BC = [2 0; 1 3]. What is (AB)C?
Answer: D
By the associative property, (AB)C = A(BC) = [1 1; 0 1][2 0; 1 3] = [3 3; 1 3], so you do not need B and C separately. Choice A computes (BC)A, which reverses the order. Choice C ignores A.
Question 10 of 20 · Multiple Choice
Let A = [1 2; 0 1]. You know that B + C = [3 0; -1 2]. What is AB + AC?
Answer: A
By the left distributive property, AB + AC = A(B + C) = [1 2; 0 1][3 0; -1 2] = [1 4; -1 2]. Choice B computes (B + C)A, with A on the wrong side. Choice C adds A to B + C instead of multiplying.
Question 11 of 20 · Multiple Choice
Simplify 3AB + BA - AB for square matrices A and B.
Answer: C
Only like terms combine: 3AB - AB = 2AB, and BA is a different matrix, so the result is 2AB + BA. Choices A and B treat BA as if it were AB, which assumes the matrices commute. Choice D combines the terms with the wrong coefficients.
Question 12 of 20 · Multiple Choice
Why is (A - B)(A + B) not always equal to A² - B² for matrices?
Answer: B
The distributive property gives A(A + B) - B(A + B) = A² + AB - BA - B². For numbers the middle terms cancel, but for matrices AB - BA is often not zero. Choice C is false: the distributive property does hold. Choices A and D are false for square matrices.
Question 13 of 20 · Multiple Choice
Let A = [1 0; 0 0] and B = [0 1; 0 0]. Which statement is true?
Answer: C
AB = [1(0) + 0(0), 1(1) + 0(0); 0, 0] = [0 1; 0 0], while BA = [0(1) + 1(0), 0; 0, 0] = [0 0; 0 0]. The two orders give different matrices. Choice D has the two products switched, and choices A and B assume the matrices commute.
Question 14 of 20 · Multiple Choice
Let A = [1 1; 0 0] and B = [1 0; 1 0]. What is AB - BA?
Answer: D
AB = [2 0; 0 0] and BA = [1 1; 1 1], so AB - BA = [1 -1; -1 -1]. Choice A would be the answer only if A and B commuted. Choice B is BA - AB, with the subtraction reversed.
Question 15 of 20 · Short Answer
Let A = [2 -1; 1 3] and B = [0 2; 1 1]. Compute AB and BA. Is AB = BA?
AB = [-1 3; 3 5] and BA = [2 6; 3 2]. They are different, so AB ≠ BA: this pair is another counterexample to commutativity.
Question 16 of 20 · Short Answer
Let A = [1 2; 0 -1], B = [1 0; 1 1] and C = [0 1; 2 0]. Compute (AB)C and A(BC).
AB = [3 2; -1 -1], so (AB)C = [4 3; -2 -1]. BC = [0 1; 2 1], so A(BC) = [4 3; -2 -1]. Both groupings give [4 3; -2 -1], as the associative property says.
Question 17 of 20 · Short Answer
Let A = [3 0; 1 2], B = [1 -1; 0 2] and C = [2 1; 1 -1]. Verify that A(B + C) = AB + AC.
B + C = [3 0; 1 1], so A(B + C) = [9 0; 5 2]. AB = [3 -3; 1 3] and AC = [6 3; 4 -1], so AB + AC = [9 0; 5 2]. Both sides equal [9 0; 5 2], as the left distributive property says.
Question 18 of 20 · Short Answer
Expand (A - B)² for square matrices A and B. When does your answer simplify to A² - 2AB + B²?
(A - B)(A - B) = A² - AB - BA + B². It equals A² - 2AB + B² only when AB = BA, because only then can -AB - BA be combined into -2AB. For most pairs of matrices, the two middle terms must stay separate.
Question 19 of 20 · Short Answer
Find the value of k for which [1 k; 0 2] and [3 1; 0 1] commute.
The first matrix times the second is [3, 1 + k; 0, 2], and the second times the first is [3, 3k + 2; 0, 2]. They are equal when 1 + k = 3k + 2, so k = -1/2. Check: with k = -1/2 both products equal [3 1/2; 0 2].
Question 20 of 20 · Short Answer
Let A = [1 0; 0 2], B = [0 1; 1 0] and C = [1 1; 0 1]. Explain why ABC needs no parentheses, then compute ABC and ACB. Are they equal?
By the associative property, (AB)C = A(BC), so ABC means the same matrix with either grouping. ABC = [0 1; 2 2] and ACB = [1 1; 2 0], which are different: associativity lets you regroup, but not reorder, because multiplication is not commutative.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSN.VM.C.9 mean?
HSN.VM.C.9 means students understand which properties of multiplication carry over from numbers to square matrices. Matrix multiplication is not commutative, because AB and BA can be different, but it is associative and distributive. The code stands for High School, Number and Quantity, Vector and Matrix Quantities, cluster C, standard 9.
Is HSN.VM.C.9 taught in Algebra 2 or Precalculus?
It is usually taught in Precalculus, right after students learn to multiply matrices (HSN.VM.C.8). HSN.VM.C.9 is a (+) standard, which Common Core describes as additional mathematics for students who take advanced courses. Some honors Algebra II courses include it in a matrices unit.
What does it mean that matrix multiplication is not commutative?
It means you cannot assume AB = BA. For numbers, the order of the factors never matters. For matrices, changing the order changes which rows are paired with which columns, so the products can be different even for two square matrices of the same size.
Do any matrices commute?
Yes, some pairs do. For example, [4 0; 0 4] commutes with every 2 × 2 matrix, because multiplying by it in either order multiplies every entry by 4. Any matrix commutes with itself, so AA = AA. "Not commutative" means the property fails for some pairs, not that it fails for every pair.
Why does the standard say "for square matrices"?
For square matrices of the same size, both AB and BA are always defined and have the same size, so the only question is whether the entries match. For non-square matrices, BA may not be defined at all, or it may have different dimensions from AB, which is a different reason the products differ.
What does the associative property let you do with matrices?
It lets you choose which product to compute first. Because (AB)C = A(BC), a product of three or more matrices can be written without parentheses. In applications, choosing a good grouping can save work, for example when one pair of matrices stays the same while another changes.
Why are there two distributive properties for matrices?
Because the factor you distribute stays on its side. For numbers, a(b + c) and (b + c)a are the same, but for matrices, A(B + C) = AB + AC and (B + C)A = BA + CA are two different statements. Both are true, but AB + AC and BA + CA are usually different matrices.
What are common mistakes with matrix properties?
Common mistakes include:
Writing 2AB in place of AB + BA
Distributing a factor onto the wrong side
Changing the order of factors while regrouping with the associative property
Concluding that a property holds because it worked for one example
How can students show that a matrix property is always true?
By using letter entries. For 2 × 2 matrices, write A = [a b; c d] and similar forms for B and C, then compute both sides and compare every entry. Numerical examples build confidence, but only a general computation or an argument shows that the property holds for all matrices.
How does HSN.VM.C.9 connect to later math?
When students use matrices to transform the plane (HSN.VM.C.12), the order of multiplication decides the order of the transformations, so a rotation followed by a reflection can differ from the reflection followed by the rotation. When solving AX = B with an inverse (HSA.REI.C.9), students must multiply by the inverse on the correct side. HSN.VM.C.10 then studies the zero and identity matrices, which play the roles of 0 and 1.
07
Related Standards
6 standards
These standards connect to HSN.VM.C.9: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
HSN.VM.C.8Prerequisite
Add, subtract and multiply matrices of appropriate dimensions
