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Consider the 222-by-222 matrix A=(51−13).A = \begin{pmatrix} 5 & 1 \\ -1 & 3 \end{pmatrix}. A=(5−113). What is the trace of A100?A^{100}?A100?
Note: The trace of a 222-by-222 matrix is defined as Tr(abcd)=a+d .\text{Tr}\begin{pmatrix} a & b \\ c& d \end{pmatrix} = a+d\; .Tr(acbd)=a+d.
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