If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to
(I + A)3 = I3 + A3 + 3A2I + 3AI2 (Using the identity of (a + b)3 = a3 + b3 + 3ab (a + b))
(I + A)3 = I + A2(A) + 3AI + 3A [I stands for Identity Matrix]
(I + A)3 = I + A2 + 3A + 3A
(I + A)3 = 7A + I
(I + A)3 – 7A
7A + I – 7A
= I
Option (C) is the answer.