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If Aa n dB are two square matrices such ...

If `Aa n dB` are two square matrices such that `B=-A^(-1)B A ,t h e n(A+B)^2` is equal to `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

AI Generated Solution

To solve the problem, we need to show that if \( B = -A^{-1}BA \), then \( (A + B)^2 = A^2 + B^2 \). ### Step-by-Step Solution: 1. **Start with the expression for \( (A + B)^2 \)**: \[ (A + B)^2 = (A + B)(A + B) \] ...
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