# Stability of a fixed point of planar system

Study the stability of the fixed point $$(0,0)$$ of the following planar linear difference system: $$x_{k+1}=\frac{3}{5}x_k+\frac{1}{5}y_k, \ y_{k+1}=\frac{1}{5}x_k+\frac{3}{5}y_k$$

Can somebody give me some ideas, please?

Study the eigenvalues of the system $$X_{n+1} = AX_n$$, where $$X_n = \begin{bmatrix} x_n \\ y_n \\ \end{bmatrix}$$ and $$A = \begin{bmatrix} \frac{3}{5} & \frac{1}{5} \\ \frac{1}{5} & \frac{3}{5} \\ \end{bmatrix}$$