# Common Core: High School - Number and Quantity : Understanding the Multiplication Concept in Matrices as the Associative and Distributive Properties: CCSS.Math.Content.HSN-VM.C.9

## Example Questions

### Example Question #1 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

Which of the following properties does not apply to matrices?

Distributive

Associative

Commutative

Commutative

Explanation:

Commutative does not apply to matrices because if we have matrices , and . It is not necessarily true that , even though in some cases it's true.

### Example Question #222 : High School: Number And Quantity

Which is an example of two matrices satisfying the associative and distributive properties? Let a be a scalar, and AB, and C be three unique matrices.

Explanation:

is the correct answer because it is the only answer that involves both the associative and distributive properties.

### Example Question #3 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

Which matrix when multiplied with

will yield the same result regardless of the order in which they're multiplied?

Explanation:

The only matrix that works is , because regardless of the order of matrix multiplication, the result will always be .

### Example Question #4 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

Why doesn't the commutative property hold for matrix multiplication?

Order of multiplication matters

Commutative property doesn't work for regular multiplication

Order of multiplication matters

Explanation:

The reason that the commutative property doesn't apply to matrix multiplication is because order of multiplication matters. We multiply by the entry in the row of the first matrix by the entry in the column of the second matrix.

### Example Question #1 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

Which is an example of two matrices satisfying the distributive properties? Let  be a scalar, and ,, and  be three unique matrices.

Explanation:

The only answer that satisfies the distributive property is

### Example Question #6 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

True or False: If  and  are square matrices, is ?

False

True

True

Explanation:

Let

.

Now do matrix multiplication inside the parenthesis.

Now multiply the result by the other matrix to get

Now lets do it from the other side

Do the matrix multiplication inside the parenthesis first

Now multiply the result by the other matrix to get

If we rearrange the terms in this matrix we get

Since these are the same matrix, we have evidence that the statement is true, .

### Example Question #7 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

True or False: The following matrix product is possible.

False

True

False

Explanation:

The answer is false because the dimensions are  for each matrix.

### Example Question #2 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

True or False:

The following matrix multiplication is possible.

True

False

True

Explanation:

The matrix multiplication is possible since the dimensions will work out. The result will be a  since the dimensions are , and .

### Example Question #2 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

True or False:

The following matrix multiplication is possible

True

False

True

Explanation:

The matrix multiplication is possible because the dimensions work out. The resulting matrix will be , because the matrices are , and .

### Example Question #3 : Understanding The Multiplication Concept In Matrices As The Associative And Distributive Properties: Ccss.Math.Content.Hsn Vm.C.9

True or False:

The following matrix multiplication is possible.