I found the following identities about Pauli matrices from the lecture notes of Supersymmetry.




Please give me some hints on how to derive the above identities.

For the first identity, if we take $\mu=0$, then $\sigma^{0}\equiv 1$, which is real. Then, the identity says


Why does the complex conjugation acting on this identity matrix $1_{2\times 2}$ exchange the two spinorial indices? Where does the minus sign come from?


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