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Please do both: a. Suppose that A ∈ Mn is non-singular. Prove that if λ ∈...

Please do both:

a. Suppose that A ∈ Mn is non-singular. Prove that if λ ∈ σ(A), then λ −1 ∈ σ(A−1 ).

b. If λ ∈ σ(U) and U ∈ Mn is unitary, show that |λ| = 1.

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