<s>[INST] Matrix $\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$ to a large power Compute
$\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}^{99}$
What is the easier way to do this other than multiplying the entire thing out?
Thanks
 [/INST] Following the comment of Matt Samuel:
$$
\begin{pmatrix}
1 & 1 \\
0 & 1 
\end{pmatrix}
\begin{pmatrix}
1 & 1 \\
0 & 1 
\end{pmatrix} = 
\begin{pmatrix}
1 & 2 \\
0 & 1 
\end{pmatrix}
$$
$$
\begin{pmatrix}
1 & 1 \\
0 & 1 
\end{pmatrix}^3
= 
\begin{pmatrix}
1 & 3 \\
0 & 1 
\end{pmatrix}
$$
$$
\begin{pmatrix}
1 & 1 \\
0 & 1 
\end{pmatrix}
\begin{pmatrix}
1 & n \\
0 & 1 
\end{pmatrix}
=
\begin{pmatrix}
1 & n+1 \\
0 & 1 
\end{pmatrix}
$$
</s>