If A is symmetric matrix, then ${B^\prime }AB$ is…………

If A is a symmetric matrix, then ${B^\prime }AB$ is a symmetric metrix.

${\left[ {{B^\prime }AB} \right]^\prime } = {\left[ {{B^\prime }(AB)} \right]^\prime }$

$= {(AB)^\prime }{\left( {{B^\prime }} \right)^\prime }$

$= {B^\prime }{A^\prime }B$
$= \left[ {{B^\prime }{A^\prime }B} \right]$

Therefore, ${B^\prime }AB$ is a symmetric matrix.