Show that  Also, find 

To show that \( A^2 - 4A + 51_{2} = 0 \), let's first calculate each term:

1. \( A^2 \):
\[ A^2 = A \times A = \left( \begin{matrix} 3 & -1 \\ 2 & 1 \end{matrix} \right) \times \left( \begin{matrix} 3 & -1 \\ 2 & 1 \end{matrix} \right) \]
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