Question
Wed April 20, 2011 By: Srinu Pattnaik

If A and B are symmetric matrices of same order,then show that AB is symetric if and only if A and B commute, that is AB=BA? please explain..

Expert Reply
Wed April 20, 2011
A and B are symmetric matrices
so A' =A and B'=B  (i)
To Prove (AB)' AB
Now (AB)' = B'A' (by property of transpose of matrices)
=BA .using (i)
So AB is symmetric iff AB =BA.
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Thankyou Mrs. Sneha Shidid .

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