If A and B are two square symmetric matrices of same order, then $AB-BA$ is

a skew-symmetric matrix

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.