Matrix reaised to an exponent $If\quad the\quad matrix\quad A\quad =\quad \begin{bmatrix} 1 & \quad -1 \\ -1 & \quad \quad 1 \end{bmatrix}\\ \qquad Then\quad { A }^{ n+1 }\quad =\quad ?$
My effort
So i tries tried raising it to the 2nd 3rd and 4th power to identify a pattern .
I was not able to identify any pattern
I also Tried writing it in terms of an identity matrix.

$$A^2=\begin{pmatrix}2&\!-2\\\!-2&2\end{pmatrix}\;,\;\;A^3=\begin{pmatrix}4&\!-4\\\!-4&4\end{pmatrix}$$
Can you see a pattern? Good, now prove it by induction.
