A groupoid G whose elements satisfy the left invertive law:
(ab)c=(cb)a is known as Abel-Grassman's groupoid (AG-groupoid).
It is a nonassociative algebraic structure midway between a
groupoid and a commutative semigroup. In this note, we show that
if G is a finite AG-groupoid with a left zero then, under
certain conditions, G without the left zero element is a commutative group.