If A is a square matrix and I is an identity matrix of same order such that $A^2=A$, then $(2I+A)^2 - 5A$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4I
Given $A^{2}=A$
Compute $(2I+A)^{2}$
$(2I+A)^{2}=4I+4A+A^{2}$
Since $A^{2}=A$:
$=4I+4A+A$
$=4I+5A$
Now compute $(2I+A)^{2}-5A$
$=4I+5A-5A$
$=4I$
$4I$