If A is a square matrix and A^2=A, then (I+A)^2-3 A is equal to - Vidyadip

MCQ

If $A$ is a square matrix and $A^2=A,$ then $(I+A)^2-3 A$ is equal to

✓
$I$
B
$A$
C
$2A$
D
$3I$

✓

Answer

Correct option: A.

$I$

Given that $A^2=A$
Consider $(I+A)^2-3 A=I^2+A^2+2 A I-3 A$
$=I+A+2 A-3 A \ \left[\because I^2=I, A^2=A \text { (given) }\right]$
$=I$

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