Wombat Game

Lemme teach you guys a game that envolves a secret. No search material please.
Two players.
Player 1 - Listen, if I am wombat, are you wombat?
Player 2 - Yes.
Player 1 - Correct. If you are wombat, am I wombat?
Player 2 - Yes.
Player 1 - Wrong.
Figure out the rule and solve this. *DON'T COPY ANSWERS, THINK OF YOUR OWN. I DON'T CARE IF YOU HAVE THE SAME ANSWER AS SOMEONE ELSE, BUT YOU NEED TO FIGURE OUT THE ANSWER, NOT COPY!*
Solve these:
If I am wombat, are you wombat?
If Smily is wombat, am I wombat?
Listen, if I am wombat, is smily wombat?
If you are wombat, amd I wombat?