In this worksheet, we will practice using the properties of matrix multiplication.

**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 Is ?

- Ano
- Byes

**Q4: **

Are the following matrices multiplicative inverses of each other?

- Ayes
- Bno

**Q5: **

Given the matrices and , is ?

- Ayes
- Bno

**Q6: **

Given the matrices and , is ?

- Ayes
- Bno

**Q7: **

Given that matrices and , is ?

- Ayes
- Bno

**Q8: **

State whether the following statement is true or false: If and are both matrices, then is never the same as .

- Afalse
- Btrue

**Q9: **

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

- Ayes
- Bno

**Q10: **

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

- A
- B
- C
- D
- E

**Q11: **

State whether the following statement is true or false: If is a matrix and and are matrices, then .

- Atrue
- Bfalse

**Q12: **

Suppose that , and .

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

Express in terms of and .

- A
- B
- C
- D
- E

**Q13: **

Given that is it true that ?

- Ayes
- Bno

**Q14: **

From the following, choose two matrices, and , such that , , and .

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

**Q15: **

Consider the matrices By setting equal to the zero matrix, find matrices and such that if , then for some numbers , and .

- A
- B
- C
- D
- E

**Q16: **

Suppose and is an invertible matrix. Does it follow that ?

- A yes
- B no

**Q17: **

Given that and is the identity matrix of the same order as , find and .

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

**Q18: **

From the following, choose two matrices, and , such that , with .

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

**Q19: **

If and are symmetric matrices, then the product is also symmetric only when and are .

- A Hermitian matrices
- B square matrices
- C invertible matrices
- D matrices that commute

**Q20: **

Let , and

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

Find .

- A
- B
- C
- D
- E

**Q21: **

What is the value of for any matrix ?

- A
- B
- C
- D

**Q22: **

If the matrices and both have order , then what is the order of the matrix ?

- A
- B
- C
- D

**Q23: **

Find a matrix such that for all matrices .

- A
- B
- C
- D
- E

**Q24: **

Let be a matrix whose entries are all zero. If is any matrix and is any matrix, which of following is equivalent to ?

- A
- B
- C
- D
- E

**Q25: **

Given that is it true that ?

- Ayes
- Bno