If A and B are symmetric matrices of the same order, then - Vidyadip

Question

If $A$ and $B$ are symmetric matrices of the same order, then

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Answer

$\text {(c) : }(A B+B A)^T$$=(A B)^T+(B A)^T$
$=B^T A^T+A^T B^T=B A+A B=A B+B A$
$\qquad\left(\because A^T=A \text { and } B^T=B\right)$
Hence, $A B+B A$ is a symmetric matrix.

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