If A and B are two square symmetric matrices of same order, then $AB-BA$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → a skew-symmetric matrix
Given: $A$ and $B$ are symmetric square matrices of the same order.
To find the nature of $AB - BA$, compute its transpose:
$(AB - BA)^T = (AB)^T - (BA)^T = B^T A^T - A^T B^T$
Since $A$ and $B$ are symmetric, $A^T = A$ and $B^T = B$, so:
$(AB - BA)^T = BA - AB = - (AB - BA)$
Therefore: $AB - BA$ is a skew-symmetric matrix.