Conditions under which Commutative Semigroup is Group/Statement of Conditions

Statement of Conditions under which Commutative Semigroup is Group
Let $\struct {S, \circ}$ be a commutative semigroup.

Let $\struct {S, \circ}$ have the following properties:


 * $(1): \quad \forall x \in S: \exists y \in S: y \circ x = x$


 * $(2): \quad \forall x, y \in S: y \circ x = x \implies \exists z \in S: z \circ x = y$