# Lesson Worksheet: Matrix Multiplication Mathematics

In this worksheet, we will practice identifying the conditions for matrix multiplication and evaluating the product of two matrices if possible.

**Q11: **

Consider the matrix product

What can you conclude about it?

- AFor a given matrix , there cannot be any matrix except the identity matrix for which .
- BFor a given matrix , there can be a matrix that is not the identity matrix for which .
- CFor a given matrix , there can be a matrix that is not the identity matrix for which .
- DFor a given matrix , there can be a matrix that is not the identity matrix for which .

Is it possible to find a matrix with the above property for every matrix ?

- ANo
- BYes

**Q13: **

Consider the matrices Find if possible.

- A
- B
- C
- D

**Q19: **

Is it possible to have a matrix and a matrix such that If so, give an example.

- AYes, ;
- BNo
- CYes, ;

**Q20: **

Suppose the matrix product makes sense. We also know that has 2 rows, has 3 columns, and has 4 entries. Is it possible to determine the possible sizes of these matrices? If so, what are the possible sizes of , , and ?

- AYes, , , ; , , ; , ,
- BYes, , , ; , , ; , ,
- CYes, , , ; , , ; , ,
- DNo
- EYes, , , ; , , ; , ,

**Q21: **

Find the matrices and such that, for any matrix , and . Explain why and are not the same.

- A, , and have different dimensions.
- B, , and have different dimensions.
- C, , and have different dimensions.
- D, , and have different dimensions.
- E, , and have different dimensions.

**Q24: **

Suppose is a matrix, is a matrix, and is a matrix. What are the sizes of the product matrices , and ?

- A
- B
- C
- D
- E

**Q25: **

If is a matrix of order and is a matrix of order , then what is the order of ?

- A
- B
- C
- D