jmc

We have that $$\begin{array}{rl}{\left(\begin{array}{cc}1& -1\\ 1& 0\end{array}\right)}^3& =\left(\begin{array}{cc}1& -1\\ 1& 0\end{array}\right)\left(\begin{array}{cc}1& -1\\ 1& 0\end{array}\right)\left(\begin{array}{cc}1& -1\\ 1& 0\end{array}\right)\\ & =\left(\begin{array}{cc}0& -1\\ 1& -1\end{array}\right)\left(\begin{array}{cc}1& -1\\ 1& 0\end{array}\right)\\ & =\boxed{\left(\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right).}\end{array}$$