Solution
= Solution
Direct <matrix multiplication> gives
$$
\tau_1^2=\tau_2^2=\tau_3^2=I_2.
$$
For 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>:
$$
\boxed{\tau_j^{2m}=I_2,\qquad\tau_j^{2m+1}=\tau_j.}
$$
These are the standard <Pauli matrices>, each a <Hermitian matrix> and an <involution>.