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
$1-A$
✓
$1$

✓

Answer

Correct option: D.

$1$

We have, $(I+A)^3-7 A$
$=I^3+A^3+3 I^2 A+3 I A^2-7 A=1+A \cdot A+3 A+3 A-7 A$
$=1+A+3 A+3 A-7 A=1$

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