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Hi could some one please help. I am having problems proving this.

Let $A$ be an $n \times n$ matrix with complex entries and let $f (t) =\det(A - tI)$ be its characteristic polynomial.

Prove that $f(A) = 0$.

Thank you!!

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user73807
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    It's called the Cayley-Hamilton Theorem. Search this website, I'm sure you'll find where it has been answered before. See, e.g., http://math.stackexchange.com/questions/362156/linear-algebra-characteristic-polynomial? – Gerry Myerson Apr 22 '13 at 13:08
  • Don't, however, arrive at $f(A) = det(A-AI) = det(0) = 0$. – Ross B. Apr 22 '13 at 14:34

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