If A & B are symmetric matrices of same order, then show that AB is symmetric if & only if A & B commute, i.e AB = BA

Given that A and B are symmetric

Therefore.. A=A'  and B=B'

To prove: (AB)=(AB)'

R.H.S.=(AB)'

           =B'A'    [ because (AB)'= B'A' ]

           =BA     [ because A=A' and B=B' is given ]

           =AB     [ because AB=BA given ]

R.H.S.= L.H.S.

Hence Proved..

Hope u got..

Gud luck.. :))))

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