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Question
If A and B are symmetric matrices of same order, prove that AB + BA is a symmetric matrix
Solution
Given A and B are symmetric matrices
⇒ – AT = A and BT = B
To prove AB + BA is a symmetric matrix.
Proof: Now (AB + BA)T = (AB)T + (BA)T
= BTAT + ATBT
= BA + AB
= AB + BA
i.e. (AB + BA)T = AB + BA
⇒ (AB + BA) is a symmetric matrix
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