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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} $

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Solution :
given $A^2=A$
$\qquad= 7A-[I+3A+3A+A^2.A]$
$\qquad= 7A-[I+3A+3A+A]$
$\qquad= 7A-I+7A$
$\qquad= -I$
answered Feb 15 by meena.p

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