If \( A \) and \( B \) are two skew-symmetric matrices, then \( AB + BA \) is:
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- a skew symmetric matrix
- a symmetric matrix
- a null matrix
- an identity matrix
The Correct Option is B
Solution and Explanation
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.
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