Question

if A and B are symmetric matrix of the same order prove that the product matrix is symmetric if A and B commute
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Answer 1

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.