Group of Units is Group

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

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

Hence the justification for referring to the group of units of $\left({R, +, \circ}\right)$.

Proof
Follows directly from Invertible Elements of Monoid form Subgroup.