Question

If \( A \) and \( B \) are skew-symmetric matrices of same order, then \( AB - BA \) is a _____

• A. Skew symmetric matrix
• B. Zero matrix
• C. Symmetric matrix
• D. Identity matrix

Hint:

If \( M^T = -M \), then matrix is skew-symmetric.

Answer 1

The Correct Option is A

Concept: For skew-symmetric matrices: \[ A^T = -A, \quad B^T = -B \]
Step 1: Take transpose. \[ (AB - BA)^T = B^T A^T - A^T B^T \] \[ = (-B)(-A) - (-A)(-B) \] \[ = BA - AB = -(AB - BA) \]
Step 2: \[ \Rightarrow (AB - BA)^T = -(AB - BA) \] \[ \Rightarrow \text{Skew symmetric} \]