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 \[\text{Tr}\begin{pmatrix} a & b \\ c& d \end{pmatrix} := a+d\; .\]

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