Question: Show that the following are equivalent for a symmetric matrix A. (a) A is orthogonal. (b) A2 = I. (c) All eigenvalues of A are

Show that the following are equivalent for a symmetric matrix A.
(a) A is orthogonal.
(b) A2 = I.
(c) All eigenvalues of A are ±1. [For (b) if and only if (c), use Theorem 2.]

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