Beaming to Mars?

A couple of weeks ago in class we had a discussion on being beamed up onto mars. Would that mean our body replicates and another form of ourself is put on Mars to live...or does our body on earth because erased and we transport to mars...or are we destroyed on eart and recreated on mars? Are we the same person on earth as we are on mars?! I'm not sure what I think. If it were possible to clone yourself and be on Mars I would want to be the same version of myself. But is that possible. Is it possible to be the same EXACT person in two places...I'm not too sure. I've never really thought about being recreated, or replicated. Would we age the same...would be turn into the same person living on two different planets. I do not think I would enjoy being destroyed and then recreated some place else. I would rather just be transported and then brought back to earth when I wanted my trip to be over.