see

Complex Matrix Stability

Insight

A_unstable : spectral radius 2 -> unstable
A_stable : spectral radius 1 -> marginally stable
A_damped : spectral radius 0 -> damped

Explanation

For a discrete-time linear system x_{k+1} = A x_k, the eigenvalues of A govern the modal behaviour.
Because the matrices are diagonal, the eigenvalues are the diagonal entries; the largest modulus gives the spectral radius and therefore the stability class.