If `A` and `B` are symmetric matrices, then show that `A B` is symmetric iff `A B=B A` i.e. `A` and `B` commute.

Explanation

To show that the product of two symmetric matrices \( A \) and \( B \) is symmetric if and only if \( A \) and \( B \) commute (i.e., \( AB = BA \)), we will break the proof into two parts.

### Part 1: If \( AB = BA \), then \( AB \) is symmetric.

1. **Start with the definition of symmetric matrices**: A matrix \( M \) is symmetric if \( M^T = M \).

2. **Consider the product \( AB \)**: We need to show that \( (AB)^T = AB \).

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