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If \( P \) and \( Q \) are symmetric matrices of the same order then \( P Q-Q P \) is
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skew symmetric matrix
(B)
Given $P=P^{\prime}$ and $Q=Q^{\prime}$
$(P Q-Q P)^{\prime}=(P Q)^{\prime}-(Q P)^{\prime}$
$=\left(Q^{\prime} P^{\prime}-P^{\prime} Q^{\prime}\right)$
$=Q P-P Q$
$=-[P Q-Q P]$
$\therefore(P Q-Q P)$ is skew symmetric.
Given $P=P^{\prime}$ and $Q=Q^{\prime}$
$(P Q-Q P)^{\prime}=(P Q)^{\prime}-(Q P)^{\prime}$
$=\left(Q^{\prime} P^{\prime}-P^{\prime} Q^{\prime}\right)$
$=Q P-P Q$
$=-[P Q-Q P]$
$\therefore(P Q-Q P)$ is skew symmetric.
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