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  4. If A and B are two square matrices such that B = - A-1 BA, then (A + B)2 =

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Q. If A and B are two square matrices such that $B = - A^{-1}\, BA$, then $(A + B)^2 =$

Matrices

Solution:

$B=-A^{-1}\,BA \Rightarrow AB=-BA \Rightarrow AB+BA=0$
$\therefore \left(A+B\right)^{2}=A^2 +AB+BA+B^{2}=A^{2}+B^{2}$