Build a matrix norm on 2x2 matrices such that for given $A$ we have that $||A^n||$ converges

Question

$$A = \begin{pmatrix} -0.5 & 0\\ 0 & 1.3 \end{pmatrix} $$

Build a matrix norm on $2 \times 2$ matrices such that for the given $A$ we have that $\|A^n\|$ converges or prove that such norm doesn't exist.