# Matrix demonstration $A^k$

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 $$k \in \mathbb{N}$$