for those that think the movie is left open to speculation, well you clearly didn't understand the point of the movie or book.
For me this is clearest in the scene where he returns to a friend's flat where he'd committed murders, only to find it being redecorated and put on the market. He meets an estate agent who initially thinks he's a prospective tenant, but then she remembers it's not been advertised yet. Then he and she both know that he's the cause of all the blood stains she's had to get cleaned up. She just asks him to leave. The flat is worth a million dollars a year in rent, but no-one will want it if they learn about the murders. Best to say nothing.