Definition:Group of Units

Theorem
Let $$\left({R, +, \circ}\right)$$ be a ring with unity.

Then the set $$U_R$$ of units of $$\left({R, +, \circ}\right)$$ forms a group under $$\circ$$.

This group $$\left({U_R, \circ}\right)$$ is called the group of units of the ring.

Proof
This follows directly from Invertible Cancellable Elements of Monoid form Group.