Question

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

• A. $0$
• B. $A^2+B^2$
• C. $A^2+2AB+B^2$
• D. $A+B$

Answer 1

The correct option is B $A^2+B^2$

As $B=-A^{-1}BA$, we get AB = -BA or AB + BA = 0.
Now,
$(A+B{)}^2=(A+B\left)\right(A+B)$
$=A^2+BA+AB+B^2$
$=A^2+O+B^2$
$=A^2+B^2$.