If A and B are symmetric matrices of the same | vedclass

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(C) Given that $A$ and $B$ are symmetric matrices,we have:$A^{\prime} = A$ and $B^{\prime} = B$  .......... $(1)$Consider the transpose of the matrix

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Skew-symmetric matrix

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(C) Given that $A$ and $B$ are symmetric matrices,we have:$A^{\prime} = A$ and $B^{\prime} = B$  .......... $(1)$Consider the transpose of the matrix $(AB - BA)$:$(AB - BA)^{\prime} = (AB)^{\prime} - (BA)^{\prime}$Using the property $(XY)^{\prime} = Y^{\prime}X^{\prime}$,we get:$(AB - BA)^{\prime} = B^{\prime}A^{\prime} - A^{\prime}B^{\prime}$Substituting the values from $(1)$:$(AB - BA)^{\prime} = BA - AB$Factoring out the negative sign:$(AB - BA)^{\prime} = -(AB - BA)$Since the transpose of $(AB - BA)$ is equal to its negative,$(AB - BA)$ is a skew-symmetric matrix.

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

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