Sei

${\displaystyle {}M={\begin{pmatrix}0&-1\\1&0\end{pmatrix}}\,.}$

Dann ist

${\displaystyle {}{\begin{pmatrix}0&-1\\1&0\end{pmatrix}}^{2}={\begin{pmatrix}0&-1\\1&0\end{pmatrix}}{\begin{pmatrix}0&-1\\1&0\end{pmatrix}}={\begin{pmatrix}-1&0\\0&-1\end{pmatrix}}\,.}$

Ferner ist

${\displaystyle {}{\begin{pmatrix}0&-1\\1&0\end{pmatrix}}^{3}={\begin{pmatrix}-1&0\\0&-1\end{pmatrix}}{\begin{pmatrix}0&-1\\1&0\end{pmatrix}}={\begin{pmatrix}0&1\\-1&0\end{pmatrix}}\,}$

und

${\displaystyle {}{\begin{pmatrix}0&-1\\1&0\end{pmatrix}}^{4}={\begin{pmatrix}-1&0\\0&-1\end{pmatrix}}{\begin{pmatrix}-1&0\\0&-1\end{pmatrix}}={\begin{pmatrix}1&0\\0&1\end{pmatrix}}\,,}$

${\displaystyle {}4}$