Consider the set G = {±1, ±i, ±j, ±k} with multiplication given by i² = j² = k² = -1; ij = k; jk = i, ki =j; ji = -k, kj = -i, ik = -j, and the usual rules for multiplying by ± 1. Show that G is a group isomorphic to the quaternion group Q₈.