4-D Clifford Algebra with (-1,1,1,1) signature

Weyl Basis: $${\gamma }^0=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right];{\gamma }^i=\left[\begin{array}{cc}0& {\sigma }^i\\ {\sigma }^i& 0\end{array}\right]$$
Dirac Basis: $${\gamma }^0=\left[\begin{array}{cc}i& 0\\ 0& -i\end{array}\right];{\gamma }^i=\left[\begin{array}{cc}0& {\sigma }^i\\ {\sigma }^i& 0\end{array}\right]$$
Majorana Basis: $${\gamma }^0=\left[\begin{array}{cc}0& i{\sigma }^2\\ i{\sigma }^2& 0\end{array}\right];{\gamma }^1=\left[\begin{array}{cc}-{\sigma }^3& 0\\ 0& -{\sigma }^3\end{array}\right];{\gamma }^2=\left[\begin{array}{cc}0& -i{\sigma }^2\\ i{\sigma }^2& 0\end{array}\right];{\gamma }^3=\left[\begin{array}{cc}{\sigma }^1& 0\\ 0& {\sigma }^1\end{array}\right];$$
$${\gamma }_{\text{Dirac}}^{\mu }=\left[\begin{array}{cc}\frac{1}{\sqrt{2}}& \frac{i}{\sqrt{2}}\\ \frac{i}{\sqrt{2}}& \frac{1}{\sqrt{2}}\end{array}\right]{\gamma }_{\text{Weyl}}^{\mu }{\left[\begin{array}{cc}\frac{1}{\sqrt{2}}& \frac{i}{\sqrt{2}}\\ \frac{i}{\sqrt{2}}& \frac{1}{\sqrt{2}}\end{array}\right]}^{-1}$$