Apparently PS3 can but unfortunately only certain models of the console will play most games,
Here is a list of the PS3 variants from the Official Playstation US Support site that will allow you to Play PSone and PlayStation 2 Games on a PlayStation 3 & the wikipedia list of games that will work
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but it has to be an official disc not a copy one, plus you might already know this, if not then you should be aware that each console does have this region-lock mechanism, Also check on the Playstion Network Store on your console to see if you find this "PlayStation 2 System Data" or something similar which this YouTuber guy posted >
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I hope the info above helps & Have a great weekend :cheers:
*Note: You can always purchase some PS2 and PSOne detail games from the App store as well.