Answer
$A^n=\left[\begin{array}{c c} 1& n\\0&1\end{array} \right]$
Work Step by Step
We are given the matrix:
$A=\left[\begin{array}{c c} 1& 1\\0& 1\end{array} \right]$
We multiply the matrix by itself multiple times to find the given powers below:
$A^2=\left[\begin{array}{c c} 1& 2\\0& 1\end{array} \right],A^3=\left[\begin{array}{c c} 1& 3\\ 0& 1\end{array} \right],A^4=\left[\begin{array}{c c} 1& 4\\0& 1\end{array} \right]$
We notice that all the elements remain the same except for the top-right value that increases by $1$ each time. Thus, we have the general pattern:
$A^n=\left[\begin{array}{c c} 1& n\\0&1\end{array} \right]$
