Show that all positive integral powers of a symmetric matrix are symmetric.

Explanation

To show that all positive integral powers of a symmetric matrix are symmetric, we will follow these steps:

**Step 1: Define a symmetric matrix.**
A matrix \( A \) is symmetric if \( A^T = A \), where \( A^T \) is the transpose of matrix \( A \).

**Step 2: Consider a positive integer \( n \).**
Let \( n \) be a positive integer. We want to prove that \( A^n \) is symmetric, which means we need to show that \( (A^n)^T = A^n \).

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