Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 2 - Section 2.6 - Matrices - Exercises - Page 184: 22

Answer

$AA^t$ is symmetric.

Work Step by Step

Given : $A$ is symmetric To Prove: $AA^t$ is symmetric Proof: Let us use $(AB)^t=B^tA^t$ and $(A^t)^t=A$ $$(AA^t)^t=(A^t)^tA^t=AA^t$$ Since the transpose of the matrix $AA^t$ results in the matrix $AA^t$ itself. $AA^t$ is symmetric.
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