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

If A and B are two square matrices such that `B=-A^(-1)BA`, then `(A+B)^(2)` is equal to

A

O

B

`A^2+B^2`

C

`A^2+2AB+B^2`

D

A + B

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`B=-A^(-1)BA`
`rArr AB=-A(A^(-1)BA)`
`rArr AB=-((A A^(-1))(BA))`
`rArr AB=-(I(BA))`
`rArr AB=-BA`
`rArr AB+BA=O`
Now,
`(A+B)^2=(A+B)(A+B)`
`rArr (A+B)^2=A^2+AB+BA+B^2`
`rArr (A+B)^2=A^2+O+B^2`
`rArr (A+B)^2=A^2+B^2`
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