I've been browsing over some Linear Algebra this summer, and came across this problem in a practice book. Any help on this? It should be solvable using only elementary methods.

Let A be an nxn matrix with characteristic polynomial

$\displaystyle f(t)=(-1)^{n}t^{n}+a_{n-1}t^{n-1}+...+a_{1}t+a_{0}$

Prove that A is invertible if and only if $\displaystyle a_{0}$ is not equal to 0.