Question

If \( A \) and \( B \) are square matrices of the same order, then \( (A B^T - B A^T) \) is a:

• A. Symmetric matrix
• B. Skew-symmetric matrix
• C. Null matrix
• D. Unit matrix

Hint:

To check if a matrix is skew-symmetric, verify if its transpose is equal to the negative of the original matrix.

Answer 1

The Correct Option is B

Step 1: Understanding skew-symmetric matrices.
A matrix is skew-symmetric if \( A = -A^T \), meaning the matrix is equal to the negative of its transpose. We are given the expression \( A B^T - B A^T \). Step 2: Checking the transpose.
Take the transpose of \( A B^T - B A^T \): \[ (A B^T - B A^T)^T = (B A^T)^T - (A B^T)^T = A B^T - B A^T \] Since the transpose of the matrix is equal to its negative, the matrix is skew-symmetric.