If P and Q are symmetric matrices of the same | vedclass

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(B) Given that $P$ and $Q$ are symmetric matrices,we have $P^{\prime} = P$ and $Q^{\prime} = Q$. To determine the nature of $PQ - QP$,we take its tran

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skew symmetric matrix

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(B) Given that $P$ and $Q$ are symmetric matrices,we have $P^{\prime} = P$ and $Q^{\prime} = Q$. To determine the nature of $PQ - QP$,we take its transpose: $(PQ - QP)^{\prime} = (PQ)^{\prime} - (QP)^{\prime}$ Using the property $(AB)^{\prime} = B^{\prime}A^{\prime}$,we get: $(PQ - QP)^{\prime} = Q^{\prime}P^{\prime} - P^{\prime}Q^{\prime}$ Since $P^{\prime} = P$ and $Q^{\prime} = Q$,this becomes: $(PQ - QP)^{\prime} = QP - PQ$ $(PQ - QP)^{\prime} = -(PQ - QP)$ Since the transpose of the matrix is equal to its negative,$PQ - QP$ is a skew-symmetric matrix.

If $P$ and $Q$ are symmetric matrices of the same order,then $PQ - QP$ is

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