Q. If $A$ is a square matrix such that $A^{2} = A$, then $(I + A)^{3} - 7A$ is
A) $3I$
B) $O$
C) $I$
D) $2I$
Explanation
(c)
Given$A^{2} = A$. Now,
$(I + A)^{3} - 7A = I^{3} + 3I^{2}A + 3IA^{2} + A^{3} - 7A$
$= I + 3A + 3A + A - 7A$
$= I + O$
$= I$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.