Do ps2 games work on a ps3?

Are ps2 games working on ps3 ???

I read online...
'The majority of them do, however there is a chunk of titles that do not work. This will probably be fixed with a patch at some point.'

'Most PS2 games will work on PS3. There have been reports of a couple older games not working properly with the new processor.'

'While the vast majority of PS2 and PS1 titles work on the new PS3, the system is not 100% backward compatible. Some of the stand out games that do not work properly on the new system are several titles from the Final Fantasy series (Origins, Chronicles, FF7, FF8, FF11), and Metal Gear Solid 3.
To check if a game you own will have compatibility issues, simply visit the site below and type in the name of the title in question.
The good news is, while not all games work on the PS3 as of launch, Sony can potentially fix this problem through new firmware patches to the system.
For more information, check Sony's official backward compatibility list website: http://www.us.playst...'