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If A and B are symmetric matrices of the same order, prove that AB + BA is symmetric

If A and B are symmetric matrices of the same order, prove that AB + BA is symmetric

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1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
A matrix A is said to be symmetric if A = AT
Now, A and B are symmetric matrices, so we have
A = AT
B = BT
Now consider,
(AB + BA)T = (AB)T + (BA)T
= BTAT + ATBT
= BA + AB
= AB + BA
Hence, the matrix (AB + BA) is symmetric.
Thanks & Regards
Latika Leekha
askIITians Faculty

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