Chapter 3.6, Problem 6P

The Pauli spin in quantum mechanics are $A=\left(\begin{array}{l}01\\ 10\end{array}\right),B=\left(\begin{array}{l}0-i\\ i0\end{array}\right),C=\left(\begin{array}{l}10\\ 0-1\end{array}\right)$

(You Will probably find these called m ${\sigma }_x,{\sigma }_y,{\sigma }_z$, in your quantum mechanics texts.) Show that A²=B²⁼C² a unit matrix. Also show that any two of these matrices anticommute, that is, AB = —BA, etc. Show that the commutator Of A and B, that is, AB — BA, is 2iC, and similarly for other pairs in cyclic order.