Question

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

• A. $O$
• B. $A^2+B^2$
• C. $A^2+2AB+B^2$
• D. $A+B$

Answer 1

Answer: (B)

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