Importance of key

On the night of Norton's murder, Hastings sees Norton go into his room and hears Norton use the key to lock his door. The same key is found in Norton's pocket when they find his dead body on the bed. It turns out that Poirot had the key to Norton's room because that was the room where he was originally staying, until he asked to be moved. Poirot claims to lose the key, so that the owners replace it for when Norton checks into the room. The key is what permits Poirot to murder Norton and stop Norton from murdering anyone else.