If Ais symmetric and B is skew-symmetric matrix, then which of the following is/are CORRECT ?

Options

A. `ABA^(T)` is skew-symmetric matrix
B. `AB^(T)+BA^(T)` is symmetric matrix
C. `(A+B) (A-B)` is skew-symmetric
D. `(A+I) (B-I)` is symmetric

Explanation

To solve the problem, we need to analyze the properties of symmetric and skew-symmetric matrices. Given that \( A \) is symmetric and \( B \) is skew-symmetric, we have:

1. A symmetric matrix \( A \) satisfies \( A^T = A \).
2. A skew-symmetric matrix \( B \) satisfies \( B^T = -B \).

Now, let’s evaluate the four options step by step.

### Step 1: Evaluate Option 1 - \( AB + A^T \)
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