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Question

If B is an idempotent matrix and A=IB, then

A
A2=A
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B
A2=I
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C
AB=O
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D
BA=O
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Solution

The correct options are
A A2=A
C AB=O
D BA=O
Since, B is an idempotent matrix,
B2=B .....(1)
B(IB)=O where O is a square matrix
Given A=IB .....(2)
BA=O
Multiplying (2) by B
AB=(IB)B
AB=BB2
AB=BB=O

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