Pauli matrices are involuntory

Any Pauli Matrix is also an Involuntory Operator. This is shown by direct calculation:

${\sigma }_x{\sigma }_x=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)=\left(\begin{array}{cc}0\ast 0+1\ast 1& 0\ast 1+1\ast 0\\ 0\ast 1+1\ast 0& 0\ast 0+1\ast 1\end{array}\right)=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)=I$ ${\sigma }_y{\sigma }_y=\left(\begin{array}{cc}0& -i\\ i& 0\end{array}\right)\left(\begin{array}{cc}0& -i\\ i& 0\end{array}\right)=\left(\begin{array}{cc}0\ast 0+-i\ast i& 0\ast -i+i\ast 0\\ 0\ast i+i\ast 0& i\ast -i+0\ast 0\end{array}\right)=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)=I$ ${\sigma }_y{\sigma }_y=\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)=\left(\begin{array}{cc}1\ast 1+0\ast 0& 1\ast 0+0\ast -1\\ 0\ast 1+-1\ast 0& 0\ast 0+-1\ast -1\end{array}\right)=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)=I$