Trace Of Matrix Power

Algebra Level 3

Consider the 22-by-22 matrix A=(5113).A = \begin{pmatrix} 5 & 1 \\ -1 & 3 \end{pmatrix}. What is the trace of A100?A^{100}?


Note: The trace of a 22-by-22 matrix is defined as Tr(abcd)=a+d  .\text{Tr}\begin{pmatrix} a & b \\ c& d \end{pmatrix} = a+d\; .

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