Pauli matrices have determinant -1

Pauli Matrixes have determinant $-1$ since: $\det ({\sigma }_x)=\det \left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)=0\ast 0-1\ast 1=-1$ $\det ({\sigma }_y)=\det \left(\begin{array}{cc}0& -i\\ i& 0\end{array}\right)=0\ast 0--i\ast i=-1$ $\det ({\sigma }_y)=\det \left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)=1\ast -1-0\ast 0=-1$