Stable matrices and their determinants

[Tonyt88]

Homework Statement

Consider a dynamical system x(t+1) = Ax(t),, where A is a real n x n matrix.
(a) If |det(A)| > or equal to one, what can you say about the stability of the zero state?
(b) If |det(A)| < 1, what can you say about the stability of the zero state?

Homework Equations

The Attempt at a Solution

I have worked with various matrices knowing if they are stable or not and the value of the determinants, but from what I can see, there exists no relation between the determinant and the stability of the matrix, so basically, where to go from here?

 

[lalbatros]

I am used to look at such questions by taking the eigenvectors as basis.
Then everything is understood on the basis of simple numbers: the eigenvalues.