If `A^(n) = 0`, then evaluate
(i) `I+A+A^(2)+A^(3)+…+A^(n-1)`
(ii)`I-A + A^(2) - A^(3) +... + (-1) ^(n-1)` for odd 'n' where I is the identity matrix having the same
order of A.

Explanation

To solve the given problem, we will evaluate two expressions based on the condition that \( A^n = 0 \).

### (i) Evaluate \( I + A + A^2 + A^3 + \ldots + A^{n-1} \)

1. **Understanding the series**: The expression \( I + A + A^2 + A^3 + \ldots + A^{n-1} \) is a finite geometric series where the last term is \( A^{n-1} \).

2. **Using the formula for the sum of a geometric series**: The sum of a geometric series can be expressed as:
\[
...