Answer
True
Work Step by Step
Since $A$ is an $n \times n$ orthogonal matrix, $A^{-1}=A^T$ (1)
We have: $AA^{-1}=AA^{-1}=I_n$ (2)
From (1) and (2), $AA^T=A^TA=I_n$
Hence, the statement is true.
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 7 - Eigenvalues and Eigenvectors - 7.5 Orthogonal Diagonalization and Quadratic Forms - True-False Review - Page 473: a
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