Show that A' A and A A' are both symmetric matrices for any matrix A.

Explanation

To show that \( A' A \) and \( A A' \) are both symmetric matrices for any matrix \( A \), we need to prove that the transpose of each matrix is equal to the matrix itself.

### Step 1: Show that \( A' A \) is symmetric

1. **Start with the expression \( A' A \)**.
- We need to take the transpose of this expression: \( (A' A)' \).

2. **Use the property of transposes**:
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