Past exam of the physics A course of the University of Cambridge / 2019 / Paper 1 / Section B / B6 / a / Solution

Write $S_i=(\hslash /2){\sigma }_i$, with ${\sigma }_i$ the Pauli matrices. Direct multiplication gives ${\sigma }_x^2={\sigma }_y^2={\sigma }_z^2=I$, and henceFor the products in the other order,Their difference gives the angular momentum commutation relationsThe first identity corresponds to the spin one-half value $s(s+1){\hslash }^2$ with $s=1/2$.