You will know soon enough without doing anything! It will be a one-sided relationship with you constantly praising and encouragining him and him never doing the same to or for you.
If he is merely a little arrogant, then the relationship may be more even and you can re-think why you considered he might be a narcissist. A narcissist only wants relationships that buoy up his self-interest ... you might say self-obsession.
There are a few definite ways to be able to tell if you are dating a narcissist. First of all, a conversation with a narcissist is always a way to feed their ego. It could be through domination, aggressive opinions, or just talking the whole time. It is generally difficult to get a word in when having a conversation with a narcissist.
Second, they are often oozing with superficial charm and arrogance. What others think of them is a top priority on their list. Because of this, they typically hang out with other high-status people since their reputation is important to them