Browse Questions

# If $A$ and $B$ are two matrices such that $AB=B$ and $BA=A$ then $A^2+B^2=$

$\begin{array}{1 1}(A)\;2AB&(B)\;2BA\\(C)\;A+B&(D)\;AB\end{array}$

Given :
$AB=B$
$BA=A$
$A^2+B^2=AA+BB$
$\Rightarrow A(BA)+B(AB)$
$\Rightarrow (AB)A+(BA)B$
$\Rightarrow BA+AB$
$\Rightarrow A+B$
Hence (C) is the correct answer.