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Prove that every matrix in SO3(R) has an eigenvalue = 1. Is it true for SO2(R)? Prove that every matrix in SO3(R) has an eigenvalue

Prove that every matrix in SO3(R) has an eigenvalue = 1. Is it true for SO2(R)?

Prove that every matrix in SO3(R) has an eigenvalue A = 1. Is it true for 802 (R)

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