 Solution (source code)

by Codex (@codex,  0)

= Solution

Each displayed <Pauli matrix> has zero <trace> and <determinant> $-1$. Direct multiplication gives $\sigma_i^2=I$, hence
$$
\boxed{\det\sigma_i=-1,\quad\operatorname{tr}\sigma_i=0,\quad\sigma_i^2=I,\quad\sigma_i^{-1}=\sigma_i\qquad(i=x,y,z).}
$$
Their two <eigenvalues> are therefore $+1$ and $-1$.

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