Only three real answers. No one can know for certain they aren't an asshole because it's really the perception of others; and many may not be willing to tell you "You're an asshole." On the flip side, you CAN know for certain you are an asshole; simply knowingly being a jerk, arguing all the time and pissing people off.
An asshole, are you one?
I'm not sure I agree with your logic on there being only three real answers. You can't know you're not an asshole because it's the perception of others? Puh-lease! As if being an asshole is a title that can only be granted by others.
What if some people perceived you as an asshole, while others disagreed. Does that make them assholes?
Can someone exist as both an asshole and a non-asshole simultaneously?
Being an asshole isn't a property of a person, but rather a state of mind. Everyone is capable of honing their inner asshole and using it to project misfortune and negativity onto others.
But to answer your question. I know I am not an asshole.