Question: Consider the equation $x ^ 2 - 5 x + 6 = 0 $ . Let its two root be $a$ and $b$ . Define

Consider the equation $x^2-5x+6=0$. Let its two root be $a$ and $b$. Define the matrix $A =\begin{pmatrix} a & 1\\0 & b \end{pmatrix}$. Calculate the determinant of $A^{100}$.

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