Can I use my T-Mobile Sim Card in an unlocked IPhone?

I just recently bought an 8gb unlocked IPhone off of Ebay. The seller didn't specify that I could put my T-mobile sim card into it and be able to use it right away. However, the seller said that she was using the phone on the T-mobile network and decided to get a new phone. I'm pretty sure I will be able to put my sim card in but could anyone please answer my question?