Question

If \( A \) and \( B \) are two skew-symmetric matrices, then \( AB + BA \) is:

• A. a skew symmetric matrix
• B. a symmetric matrix
• C. a null matrix
• D. an identity matrix

Hint:

Remember the properties of skew-symmetric matrices and their behavior under addition and multiplication.

Answer 1

The Correct Option is B

Step 1: Recall the property of skew-symmetric matrices
For a skew-symmetric matrix \( A \), \( A^T = -A \). 
Step 2: Analyze \( AB + BA \)
Taking the transpose: \[ (AB + BA)^T = B^T A^T + A^T B^T = (-B)(-A) + (-A)(-B) = AB + BA. \] Thus, \( AB + BA \) is symmetric, as its transpose equals itself.