If `A` is a skew-symmetric matrix and `n` is an even natural number, write whether `A^n` is symmetric or skew-symmetric matrix or neither of the two

Explanation

To determine whether \( A^n \) is symmetric, skew-symmetric, or neither when \( A \) is a skew-symmetric matrix and \( n \) is an even natural number, we can follow these steps:

### Step-by-Step Solution:

1. **Definition of Skew-Symmetric Matrix**:
A matrix \( A \) is skew-symmetric if \( A^T = -A \).

2. **Finding the Transpose of \( A^n \)**:
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