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Kishore Kumar

Feb 2, 2014

If A and B are symmetric matrices of the same order

If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA

Kishore Kumar

Since AB is symmetric, we have AB = (AB)T But (AB)T = BT AT Hence AB = BT AT  …(1) It is also given that A and B are symmetric AT  = A and BT = B Hence (1) becomes, AB = BA Thus AB is symmetric if and only if AB = BA.
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