CUET Preparation Today
If A and B are symmetric matrices of the same order, then AB - BA is a: |
symmetric matrix zero matrix skew symmetric matrix identity matrix |
skew symmetric matrix |
The correct answer is Option (3) - skew symmetric matrix $(AB-BA)^T$ $=(AB)^T-(BA)^T$ $=B^TA^T-A^TB^T$ $=BA-AB$ so $(AB-BA)^T=-(AB-BA)$ Hence its skew symmetric |
