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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)B A ,t h e n(A+B)^2` is equal to a.`A^2+B^2` b. `O` c. `A^2+2A B+B^2` d. `A+B`

A

`A^(2)+B^(2)`

B

`O`

C

`A^(2)+2AB+B^(2)`

D

`A+B`

Text Solution

Verified by Experts

The correct Answer is:
A
As `B=-A^(-1)BA`, we get
`AB=-BA` or `AB+BA=O`
Now,
`(A+B)^(2)=(A+B) (A+B)`
`=A^(@)+BA+BA+B^(2)`
`=A^(2)+O+B^(2)`
`=A^(2)+B^(2)`
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