Let Q be a 3×3 orthogonal matrix whose determinant is equal to 1. (a) If the eigenvalues of Q are all real and if they are ordered so that λ1 ≥ λ2 ≥ λ3, determine the value of all possible triples of eigenvalues (λ1 , λ2, λ3). (b) In the case that the eigenvalues λ2 and λ3 are complex, what are the possible values for λ1? Explain. (c)  Explain why λ = 1 must be an eigen value of Q.

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