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Question
If A and B are symmetric matrices, then write the condition for which AB is also symmetric.
Solution
Given: AB is symmetric.
`⇒( AB) ^T = AB`
`⇒ B^T A^T = AB [∵( AB)^T = B^T A^T ]`
`⇒ BA = AB [ A and \text{B are symmetric matrices}, \text{ so } A^T= A and B^T = B]`
Thus, AB is also symmetric, if AB = BA.
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