If your PS2 is fat model, it is compatible.
If your PS2 is slim model, and has a model number that is SCPH-7xxxx or lower, it is compatible.
If your PS2 is slim model, and has model number of SCPH-9XXXX with date code 8a or 8b, it is compatible. If it is 8c, it may or may not work (depends if built in 3rd quarter of 2008. )
If you have a different date code, you cannot run FMCB as Sony fixed the exploit.