Q23 of 307 Page 6

If A and B are symmetric matrices, then write the condition for which AB is also symmetric.

If A and B are symmetric matrices, then AB is symmetric if and only if A and B commute .i.e.

AB = (AB)^T = B^TA^T = BA

[∵ B^T = B and A^T = A]

If A = [a_ij] is a skew-symmetric matrix, then write the value of .

If B is a skew-symmetric matrix, write whether the matrix AB A^T is symmetric or skew-symmetric.

If B is a symmetric matrix, write whether the matrix AB A^T is symmetric or skew-symmetric.