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If B is an idempotent matrix, and A=I-B ...

If `B` is an idempotent matrix, and `A=I-B ,` then `A^2=A` b. `A^2=I` c. `A B=O` d. `B A=O`

A

`A^(2) = A`

B

`A^(2) = I`

C

`AB=O`

D

`BA= O`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`because A = I - B`
`rArr A^(2) =I^(2) + B^(2) - 2 B= I - B = A ` [ `because` B is idempotent ]
and `AB= B- B^(2) = B - B= 0 ` [ nill matrix]
and `BA = B- B^(2) = B - B = 0 ` [ null matrix]
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