?? only commenting because i am bored, your actually asking if a ps2 can play ps3 games, yes it can also your ps2 will play commodore 64 tape cassettes, nintendo 64 cartridges, the ps2 will also play xbox and xbox 360 games even wii u games!!!.
kidding, youve probably asked the most stupid question ive ever seen on this forum.
if in any chance you actually mean, can the ps3 play ps2 games, then yes it can (sort of) but personally id get a PS2 because it was never really supported by sony (they tried emulation but like the 360 BC emulation died before it begun) there are some cfw's that support this, but ive never tested it.