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Question
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
Solution
If A and B are symmetric matrices of same order, then AB is symmetric if and only if AB = BA.
Explanation:
Given that A' = A
And B' = B
Let P = AB
P' = (AB)'
= B'A'
P' = BA .....[∵ A' = A and B' = B]
= P
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