Browse Questions

# If $A$ is a square matrix such that $A^2=A$, then write the value of $7A -(I+A)^3$ where $I$ is an identity matrix.

$\begin{array}{1 1}\text{I} \\ \text{-I} \\ \text{$\pm I$} \\ \text{none of the above} \end{array}$

Solution :
given $A^2=A$
$7A-(I+A)^3=7A-[I^3+3A^2I+3AI^2+A^3]$
$\qquad= 7A-[I+3A+3A+A^2.A]$
$\qquad= 7A-[I+3A+3A+A]$
$\qquad= 7A-I+7A$
$\qquad= -I$