Question

If A is a symmetric matrix then prove that AA' is also symmetric matrix.​

Answer 1

$\large\underline{\sf{Solution-}}$

It is given that A is a symmetric matrix.

$\rm :\longmapsto\: {A}^{'} = A$

Consider,

$\rm :\longmapsto\: {(A {A}')}'$

$\rm \: = \: (A')' \: A'$

$\rm \: = \: AA'$

Therefore,

$\rm :\longmapsto\: {(A {A}')}' = AA'$

Hence, Proved.