Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 3 / a / Solution

Direct matrix multiplication givesFor example, the diagonal entries of ${\tau }_2^2$ are $(-i)i=i(-i)=1$, and its off-diagonal entries vanish. Associativity now reduces every positive integer power to its integer parity:These are the standard Pauli matrices, each a Hermitian matrix and an involution.