Задача 4.

* Show that if in Definition 2 you substitute the properties of the existance of the identity element the existence of the inverse by: $1^{\circ}) \ \exists e \in G \ \forall a \in G : ea=a$ (left identity element); $2^{\circ}) \ \forall a \in G \ \exists a^{-1} \in G : a^{-1} a = e $ (left inverse), then you will get an equivalent definition of a group.