Question: [Q2] (Section 5.2: Basic Facts about Eigenpairs; Related to Exercise 5.2.2) Let A e Rnxn (a) Show that A is an eigenvalue of A if

[Q2] (Section 5.2: Basic Facts about Eigenpairs; Related to Exercise 5.2.2) Let A e Rnxn (a) Show that A is an eigenvalue of A if and only if A is a solution of the characteris- tic equation Pn(X) = 0, where pn(A) = det(X/ - A) is the degree n characteristic polynomial associated with A. (b) Show that A is nonsingular if and only if 0 is not an eigenvalue of A

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