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Worksheet: Properties of Matrix Multiplication
Q2:
From the following, choose two matrices, and , such that , , and .
- A ,
- B ,
- C ,
- D ,
- E ,
Q3:
Are the matrices multiplicative inverses of each other?
- AYes
- BNo
Q4:
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
Q5:
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
Q6:
Given that is it true that ?
- Ayes
- Bno
Q7:
Given that is it true that ?
- Ayes
- Bno
Q8:
Consider the matrices and Is ?
- Ano
- Byes
Q9:
Suppose and is an invertible matrix. Does it follow that ?
- A yes
- B no
Q10:
Given that and is the identity matrix of the same order as , find and .
- A ,
- B ,
- C ,
- D ,
Q11:
From the following, choose two matrices, and , such that , with .
- A ,
- B ,
- C ,
- D ,
- E ,
Q12:
Given that matrices and , is ?
- Ayes
- Bno
Q13:
State whether the following statement is true or false: If is a matrix and and are matrices, then .
- Atrue
- Bfalse
Q14:
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
Q15:
Given three matrices and , which of the following is equivalent to ?
- A
- B
- C
- D
- E
Q16:
Given the matrices and , is ?
- Ayes
- Bno
Q17:
What is the value of for any matrix ?
- A
- B
- C
- D
Q18:
If the matrices and both have order , then what is the order of the matrix ?
- A
- B
- C
- D
Q19:
State whether the following statement is true or false: If and are both matrices, then is never the same as .
- Afalse
- Btrue
Q20:
Is there a matrix , other than the indentity matrix , where for every matrix ?
- Ayes
- Bno
Q21:
Find a matrix such that for all matrices .
- A
- B
- C
- D
- E
Q22:
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
Q23:
Given the matrices and , is ?
- Ayes
- Bno
Q24:
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
Q25:
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