Originally Posted by

**jameselmore91** I'm having trouble with this problem. Here is all the problem states:

Prove: **Let <A, O> be a system** (where O is the operator) **with a left identity of g and a right identity of d**. (So for all elements of A, a, aOd = a and gOa = a)

**Show that g = d.**

**As corollaries, show that a two-sided identity is unique, and if O is commutative, then <A,O> has at most one left - identity.**

I understand what they are asking for but I can't figure out how to prove it without assuming O is commutative. Thanks for the help in advance.