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Multiplication of Matrices

A and B are t...

Question

A and B are two square matrices of same order and A' denotes the transpose of A, then

A

(A B)^{'} = B^{'} A^{'}

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B

(A B)^{'} = A^{'} B^{'}

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C

A B = 0 \Rightarrow | A | = 0

or

| B | = 0

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D

A B = 0 \Rightarrow A = 0

or

B = 0

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Solution

The correct option is A $(A B)^{'} = B^{'} A^{'}$
Property of transpose of product of matrices
$(A B)^{'} = B^{'} A^{'}$

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Similar questions

Q. If square matrices

A

B

A A^{'} = A^{'} A, B B^{'} = B^{'} B, A B^{'} = B^{'} A

,
then is the statement

A B (A B)^{'} = (A B)^{'} A B

A^{'}

is transpose of

A

If true enter 1 else enter 0

Q. If A and B be two square matrices of the same order then | AB | = 0 implies

A

B

2 \times 2

matrices. Consider the statements

(i)

A B = 0 \Rightarrow A = 0 o r B = 0

(i i)

A B = I \Rightarrow A = B^{- 1}

(i i i)

(A + B)^{2} = A^{2} + 2 A B + B^{2}

A

B

2 \times 2

matrices. Consider the statements

(i) A B = 0 \Rightarrow A = 0

B = 0

(i i) A B = I_{2} \Rightarrow A = B^{- 1}

(i i i) (A + B)^{2} = A^{2} + 2 A B + B^{2}

A

B

are square matrices of the same order such that

A^{2} = A, B^{2} = B, A B = B A = 0

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