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  4. If A and B are symmetric matrices of the same order, then A B prime-B A prime is a

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Q. If $A$ and $B$ are symmetric matrices of the same order, then $A B^{\prime}-B A^{\prime}$ is a

Matrices

Solution:

$\left(A B^{\prime}-B A^{\prime}\right) =\left(A B^{\prime}\right)-\left(B A^{\prime}\right) $
$ =\left(B A^{\prime}-A B^{\prime}\right) $
$=-\left(A B^{\prime}-B A^{\prime}\right)$
$\because \left(A B^{\prime}-B A^{\prime}\right) =-\left(A B^{\prime}-B A^{\prime}\right)$
Thus, $A B^{\prime}-B A^{\prime}$ is a skew-symmetric matrix.