Schur multiplier of abelian group is its exterior square

Statement
Suppose $$G$$ is an abelian group. The Schur multiplier of $$G$$, denoted $$M(G)$$, which is the same as the second homology group for trivial group action $$H_2(G;\mathbb{Z})$$ is isomorphic to the group $$\bigwedge^2 G$$, defined as the exterior square of $$G$$ viewed as a $$\mathbb{Z}$$-module.