If A is square matrix such that A^2=A, then (I+A)^3-7 A is equal … - Vidyadip

MCQ

If $A$ is square matrix such that $A^2=A$, then $(I+A)^3-7 A$ is equal to

A
$A$
B
$1+ A$
C
$1-A$
D
1

✓

Answer

We have, $(I+A)^3-7 A$
\[\begin{array}{l}
=I^3+A^3+3 I^2 A+3 I A^2-7 A=1+A \cdot A+3 A+3 A-7 A \\
=1+A+3 A+3 A-7 A=1
\end{array}\]

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