Question

If A and B are square matrices of the same order, then $(A+B{)}^2=A^2+2AB+B^2$ implies

• A. AB = BA
• B. AB = O
• C. AB + BA = O
• D. none of these

Answer 1

Answer: (A)

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