2. (10%) $$\text{已知 } A = \begin{bmatrix} 2 & 3 \\ 4 & 1 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{-3}{5} \\ \frac{1}{\sqrt{2}} & \frac{4}{5} \end{bmatrix} \begin{bmatrix} 5 & 0 \\ 0 & -2 \end{bmatrix} \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{-3}{5} \\ \frac{1}{\sqrt{2}} & \frac{4}{5} \end{bmatrix}^{-1} \tag{2}$$ 請利用(2)的結果來求取 $\begin{bmatrix} 0.4 & 0.6 \\ 0.8 & 0.2 \end{bmatrix}^4$