# Lesson Worksheet: Properties of Matrix Multiplication Mathematics

In this worksheet, we will practice identifying the properties of matrix multiplication, including the transpose of the product of two matrices, and comparing them to the properties of multiplication of numbers.

Q1:

Given that find and .

• A,
• B,
• C,
• D,

Q2:

Matrices ,,, and are square matrices. Use the associative law for three square matrices to determine which of the following proves that .

• A
• B
• C
• D

Q3:

Consider the matrices  and . Is ?

• ANo
• BYes

Q4:

Given the matrices and , is ?

• AYes
• BNo

Q5:

Given the matrices and , is ?

• ANo
• BYes

Q6:

Given that matrices and , is ?

• AYes
• BNo

Q7:

True or False: If and are both matrices, then is never the same as .

• AFalse
• BTrue

Q8:

Is there a matrix , other than the identity matrix , where for every matrix ?

• AYes
• BNo

Q9:

Given three matrices ,, and , which of the following is equivalent to ?

• A
• B
• C
• D
• E

Q10:

True or False: If is a matrix and and are matrices, then .

• ATrue
• BFalse

This lesson includes 26 additional questions and 80 additional question variations for subscribers.