The conditions are:
- Associativity holds.
- Existence of right identity element.
- Existence of left inverse.
Can't seem to come up with any such construction. My hunch is that somehow we have to prove that there is a left identity different from the right identity, hence there are two identities. Played around with matrices with different form but all efforts fail. Please help. P.S.: This is a problem from Topics in algebra by Herstein which I am self studying.
