If A is a square matrix of order $3×3$ such that $A^2=A$ and I is the unit matrix of order $3× 3$, then the value of $(I-A)^3+A^2+I$ is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $2I$
$(I-A)^3+A^2+I$
$=I^3-A^3-3I^2A+3IA^2+A^2+I$
$=I-A-3A+3A+A+I$
$=2I$