Trace Of Matrix Power

Algebra Level 3

Consider the $2$ -by- $2$ matrix $A = \begin{pmatrix} 5 & 1 \\ -1 & 3 \end{pmatrix}.$ What is the trace of $A^{100}?$

Note: The trace of a $2$ -by- $2$ matrix is defined as $\text{Tr}\begin{pmatrix} a & b \\ c& d \end{pmatrix} = a+d\; .$