Riddle: A Liar OR a Truth Teller
This is a harder version of the famous riddle, A Liar and a Truth Teller. You should try that riddle first before solving this one.
You're walking down a path and come to two doors. One of the doors leads to a life of prosperity and happiness, and the other door leads to a life of misery and sorrow. You don't know which door is which.
In front of the door is ONE man. You know that this man either always lies, or always tells the truth, but you don't know which. The man knows which door is which.
You are allowed to ask the man ONE yes-or-no question to figure out which door to go through. To make things more difficult, the man is very self-centered, so you are only allowed to ask him a question about what he thinks or knows; your question cannot involve what any other person or object (real or hypothetical) might say.
What question should you ask to ensure you go through the good door?
An opaque hint:
1 x 1 = 1
-1 x -1 = 1
You want a question that behaves like these equations: if you're asking the truth-teller, your question has redundancy, but if you're asking the liar, multiple lies cancel each other out just like the double-negatives cancel out.