If A and B are two matrices such that...

If `A` and `B` are two matrices such that `A B=A` and `B A=B` , then `B^2` is equal to `B` (b) `A` (c) 1 (d) 0

A

BA=I

B

A

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:

A

We have, AB =A and BA =B
`:. B^2=B B`
`rArr B^2=(BA)B [ :'BA=B]`
`rArr B^2=B(AB)`
`rArr B^2=BA [ :' AB=A]`
`rArr B^2=B [:' BA=B]`

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