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If A and B are symmetric metrices of same order, then AB - BA is a |
Symmetric matrix Skew symmetric matrix Zero matrix Identity matrix |
Skew symmetric matrix |
The correct answer is Option (2) - Skew symmetric matrix Given $A^T=A,B^T=B$ so $P=(AB-BA)$ $P^T=(AB-BA)^T=(AB)^T-(BA)^T$ $=B^TA^T-A^TB^T$ $=BA-AB$ $=-(AB-BA)=-P$ $P^T=-P$ skew symmetric |
