For the matrix $A = \left( \begin{array} { l l } 1 & 0 \\ 3 & 1 \end{array} \right)$ with $A ^ { 8 } = \left( \begin{array} { l l } 1 & 0 \\ a & 1 \end{array} \right)$, find the value of $a$. [3 points]
For the matrix $A = \left( \begin{array} { l l } 1 & 0 \\ 3 & 1 \end{array} \right)$ with $A ^ { 8 } = \left( \begin{array} { l l } 1 & 0 \\ a & 1 \end{array} \right)$, find the value of $a$. [3 points]