Question: (a) Prove that every 3 3 proper orthogonal matrix has +1 as an eigenvalue. (b) True or false: An improper 3 3 orthogonal

(a) Prove that every 3 × 3 proper orthogonal matrix has +1 as an eigenvalue.
(b) True or false: An improper 3 × 3 orthogonal matrix has -1 as an eigenvalue.

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