I'm a bit stuck on where to start on this proof. The problem reads:

"Let A be an n x n matrix with characteristic polynomial:

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

Prove that A is invertible iff a(0) is not equal to Zero.

The (n-1), (1) and (0) are subscripts, my apologies I don't have/know how to use Latex to form the equations appropriately.