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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) + 2 AB + B^(2)`

D

`A + B`

Text Solution

Verified by Experts

The correct Answer is:
B
`because B=- A^(-1) BA`
` rArr AB=- BA `
`rArr AB + BA = 0 `
Now , `(A+B)^(2) =(A+B) (A+B) `
`= A^(2) + AB + BA + B^(2)`
`= A^(2) + 0 + B^(2)`
`= A^(2) + B^(2)`
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