Q72 / 180 · KCET 2019 · Mathematics

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

A
symmetric matrix
Correct answer
B
skew symmetric matrix
C
identity matrix
D
zero matrix

Solution

(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.

Hence, the correct answer is option: 'B'.

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Solution

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