Question: Problems Q1. Let A E Maxn (F). (a) Prove that if A is an eigenvalue of A, then 1 - A is an eigenvalue of

Problems Q1. Let A E Maxn (F). (a) Prove that if A is an eigenvalue of A, then 1 - A is an eigenvalue of I - A. (b) Prove, conversely, that if / is an eigenvalue of / - A, then there exists an eigenvalue > of A such that # = 1 - 1. (c) Suppose that all the eigenvalues A of A satisfy |X|

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