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## Homework Statement

Let A be any square matrix and PsubA(lambda) be its characteristic polynomial, show that

PsubA(A) = 0.

## Homework Equations

## The Attempt at a Solution

I can show this for a general 2x2 matrix case with entries a, b,c,d and understand how it would be true of all square matrices, but I'm just not sure how to show this is true for any square matrix. We are studying Jordan Canonical Form of a matrix so, I'm thinking I should somehow use that. Any help would be appreciated.