Here is my problem:

Let A be a complex n x n matrix with minimal polynomial q(x)=the sum from j=0 to m of where and = 1.

Show: If A is non-singular then does not equal 0.

So, I get that 0=q(A)= , but I'm not sure what to do here. I assume we will have to use the fact that A is non-singular, but I'm not sure how. Does it maybe involve multiplying both sides by x on the right side? Any hints would be much appreciated!