Final answer:
Alexander Hamilton had a rivalry with Aaron Burr, the person he punched at Princeton. The rivalry ended with a duel in which Burr shot and mortally wounded Hamilton.
Step-by-step explanation:
Alexander Hamilton's relationship with the person he punched at Princeton was that of a rivalry. The person in question was Aaron Burr, who was handling the financials at Princeton. The rivalry between Hamilton and Burr eventually led to a duel in 1804, where Burr shot and mortally wounded Hamilton.