Answer
See answer below
Work Step by Step
If A and B are $n ×n$ symmetric matrices then we have:
$A=A^T$
and $B=B^T$
To show that $AB=(AB)^T$
we take the right side: $(AB)^T=B^TA^T=BA=AB$
Therefore, $AB$ is symmetric.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 2 - Matrices and Systems of Linear Equations - 2.2 Matrix Algebra - Problems - Page 137: 39
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