A matrix A is not invertible if and only if 0 is an eigenvalue of A which is if and only if if and only if
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
Prove that A is invertible if and only if is not equal to 0.