Question: Let A R n,n and let be the characteristic polynomial of A. 1. Assume A is diagonalizable. Prove that A annihilates its own characteristic

Let A ∈ R^n,nand let

p(A) = det(^In A) = A + Cn-1^"-1 +...+c + co

be the characteristic polynomial of A.

1. Assume A is diagonalizable. Prove that A annihilates its own characteristic polynomial, that is

2. Prove that p(A) = 0 holds in general, i.e., also for non-diagonalizable square matrices.

p(A) = det(^In A) = A + Cn-1^"-1 +...+c + co

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