If A is square matrix such that A^ 2 =A, then (1+A)^ 3 -7 A is eq… - Vidyadip

MCQ

If $A$ is square matrix such that $A^{2}=A$, then $(1+A)^{3}-7 A$ is equal to

A
$A$
B
$I-A$
C
$3A$
✓
$I$

✓

Answer

Correct option: D.

$I$

d
$(I+A)^{3}-7 A=I^{3}+A^{3}+3 I^{2} A+3 A^{2} I-7 A$

$=I+A^{3}+3 A+3 A^{2}-7 A$

$=I+A^{2} \cdot A+3 A+3 A-7 A$ $\left[A^{2}=A\right]$

$=I+A \cdot A-A$

$=I+A^{2}-A$

$=I+A-A$

$=I$

$\therefore(I+A)^{3}-7 A=I$

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