Answered: 1. .) Let A = (aj)-1 be an n x n…

1. .) Let A = (aj)-1 be an n x n symmetric matrix (i.e. aj aji). Show, justifying your answer, that (a) if A is also orthogonal then A² = In, (b) instead, if A² = In then A is orthogonal.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.3: The Inverse Of A Matrix

Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....

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Question

1.
.) Let A = (aij)-1 be an n x n symmetric matrix (i.e. aj aji). Show, justifying your
answer, that
(a) if A is also orthogonal then A² = In,
(b) instead, if A² = In then A is orthogonal.

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