In this worksheet, we will practice multiplying matrices.

**Q4: **

Given that , find .

- A
- B
- C
- D

**Q5: **

Determine the values of , , and that satisfy the following:

- A , ,
- B , ,
- C , ,
- D , ,

**Q7: **

Consider the matrices Find , if possible.

- A
- B
- C
- D
- E It is not possible.

**Q9: **

Consider the matrices Find and if possible.

- A ,
- B ,
- C ,
- D ,
- EIt is not possible.

**Q10: **

Consider the matrices

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

**Q11: **

Suppose

Find the product .

- A
- B
- C
- D
- E

Find the product .

- A
- B
- C
- D
- E

**Q12: **

Evaluate the matrix product

- A
- B
- C
- D
- E

**Q13: **

Consider the matrix product

What can you conclude about it?

- A For a given matrix , there can be a matrix that is not 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 cannot be any matrix except 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

**Q14: **

Consider the matrices

Find and .

- A ,
- B ,
- C ,
- D ,

**Q15: **

Let and . Find and .

- A , 1
- B ,
- C ,
- D , 1
- E , 1

**Q16: **

Consider the matrices Find if possible.

- A
- B
- C
- D

**Q17: **

Given that and is the unit matrix of the same order, find the matrix for which .

**Q18: **

Given that find if possible.

- A
- B
- C
- D

**Q19: **

Given that and , find if possible.

- A
- B
- C
- D

**Q20: **

Consider the matrices Find , if possible.

- A
- B
- C
- D

**Q21: **

Given that determine if possible.

- A
- B
- C
- Dundefined

**Q22: **

Given that find the value of .

- A
- B
- C
- D9

**Q23: **

Let , .

Verify that if matrix satisfies , then and . Find matrices and so that , and then use this to find and so that

- A , .
- B , .
- C , .
- D , .
- E , .

**Q24: **

Find the values of and given

- A ,
- B ,
- C ,
- D ,

**Q25: **

Given that where is the zero matrix of order , find the values of and .

- A ,
- B ,
- C ,
- D ,