Question from the matrix theory. Prove that a matrix A is invertible if and only if zero is not an eigen value of A. Since we see if and only if in...

Question from the matrix theory.

Prove that a matrix A is invertible if and only if zero is not an eigen value of A.

Since we see if and only if in this question, we need to show by two direction. Please help me on this question, appreciated on any detail explaining.