Instructions
Turn on your Sony PlayStation 3 and let the unit load until you see its main menu system.
Use your PlayStation 3 controller to highlight the "Settings" option. Press the "X" controller button to enter the "Settings" menu.
Select "System Update."
Select "Update via Internet." Your Sony PlayStation 3 will connect to the Internet and compare the firmware it is currently running to the latest version that is available online. If a newer version is available online, it will be automatically downloaded and installed. Your Sony PlayStation 3 will reset once this installation has finished.
Insert a PlayStation 2 game disc into your newly updated Sony PlayStation 3. The PS2 game will now load just fine on your PS3.