(a) Prove that if det A 1, then A has at least one eigenvalue with 1 (b) If det A 1, are all eigenvalues 1 Prove or find a counter example

Question: (a) Prove that if det A > 1, then A has at least one eigenvalue with || > 1. (b) If |det A| < 1,

(a) Prove that if det A > 1, then A has at least one eigenvalue with |λ| > 1.
(b) If |det A| < 1, are all eigenvalues |λ| < 1? Prove or find a counter example.

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