is God necessarily triune?

About a month ago, we were discussing identity in my metaphysics class. What's interesting about identity is that because it is so difficult to define, it can more easily be defined by what it is not (ie: identity can include things such as separability/inseparability, dependence/independence, cause/effect, but it is not in every case defined by those things). We eventually discussed whether or not identity can really be separated from the idea of otherness, or if we can only really know identity by knowing otherness. Somewhere in the conversation, one of the student's attempted to use God as a counterexample, by saying that God can know himself (identity) without experiencing otherness. Following that comment, someone else used the otherness of the persons of the trinity to argue against the aforementioned claim. In responding, one of my professors offhandedly mentioned that he thought that God didn't have to exist in three persons, that he could have existed as one if he had so chosen. i'm curious what anyone else has to say in response to this. Maybe it's just me, but something seems very wrong about that statement. anyone have any critiques? comments?