  An AG-groupoid is an algebraic structure that satisfies the left invertive
law: (ab)c =(cb)a. We prove that the class of left transitive AG-groupoids
(AG-groupoids satisfying the identity, ab.ac = bc) coincides with the class of
T2-AG-groupoids. We also develop a simple procedure to test whether an
arbitrary groupoid is left transitive AG-groupoid or not. Further we prove
that, (i). Every left transitive AG-groupoid is transitively commutative
AG-groupoid (ii) For left transitive AG-groupoid the properties of flexibility,
right alternativity, AG*, right nuclear square, middle nuclear square and
commutative semigroup are equivalent.
