Given a matrix $ A = \begin{bmatrix} 7 & 4\ -9 & -5 \end{bmatrix}$ $ \in \mathcal{M2\times2}\, (\mathbb{R}) $

Show that $ A^k = \begin{bmatrix} 1+6k & 4k\ -9k & 1-6k \end{bmatrix} $ for every $ k \in \mathbb{N}$

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