Multiplicative Group of Field is Abelian Group/Proof 2

Theorem
Let $\left({F, +, \times}\right)$ be a field.

Let $F^* := F \setminus \left\{{0}\right\}$ be the set $F$ less its zero.

The algebraic structure $\left({F^*, \times}\right)$ is an abelian group.

Proof
Recall that a field is a non-trivial commutative division ring.

The result follows from Division Ring Non-Zero Elements form Group.