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..
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