For the quadratic equation $x ^ { 2 } - 4 x - 1 = 0$ with roots $\alpha$ and $\beta$, find the sum of all components of the product of two matrices $\left( \begin{array} { l l } \alpha & \beta \\ 0 & \alpha \end{array} \right) \left( \begin{array} { l l } \beta & \alpha \\ 0 & \beta \end{array} \right)$.