If `A` is a square matrix such that `A^2=A ,t h e n(I+A)^3-7A` is equal to (a)`A` (b) `I-A` (c) `I` (d) `3A`

Explanation

To solve the problem, we need to evaluate the expression \((I + A)^3 - 7A\) given that \(A^2 = A\). This means that \(A\) is an idempotent matrix.

### Step-by-step Solution:

1. **Expand \((I + A)^3\)**:
Using the binomial theorem, we can expand \((I + A)^3\):
\[
(I + A)^3 = I^3 + 3I^2A + 3IA^2 + A^3
...