Instructions
Disconnect the PS3 from the main electrical supply.
Stand the PS3 on its side and look at its bottom. The serial number is on the rectangular sticker near a line of vents. The number is clearly labeled "Model No." and is followed by a series of letters and numbers, almost always starting with "CEC." If your PS3 does not have this sticker, look on the back of the system at the barcode and find the letters "CEC."
Read the first five letters of the model number. If your model number is "CECHA," "CECHB," "CECHC," or "CECHE," your PS3 will play most PS2 games. These are the only model numbers that play PS2 games.
Follow the link in resources to visit Sony's official site and find out which PS2 games you can play on your PS3.