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

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(A) Given that $A$ and $B$ are symmetric matrices,we have $A^T = A$ and $B^T = B$. Consider the matrix $X = AB - BA$. To check if $X$ is symmetric or

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Skew symmetric matrix

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(A) Given that $A$ and $B$ are symmetric matrices,we have $A^T = A$ and $B^T = B$. Consider the matrix $X = AB - BA$. To check if $X$ is symmetric or skew-symmetric,we find its transpose: $X^T = (AB - BA)^T = (AB)^T - (BA)^T$. Using the property $(PQ)^T = Q^T P^T$,we get: $X^T = B^T A^T - A^T B^T$. Since $A^T = A$ and $B^T = B$,we substitute these values: $X^T = BA - AB = -(AB - BA) = -X$. Since $X^T = -X$,the matrix $AB - BA$ is a skew-symmetric matrix.

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

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