Question On Video (Blu-Ray and DVD) Playback.

Just got my PS3 and I have a quick question when watching a movie. On my older DVD player, and although it's probably bad to mention this, my Xbox 360, when I power down the system and then turn it back on with out taking the disc out, it saves the place on the DVD when I turned off the player. Basically so I don't have to remember and search through the chapters to find my place again in the video. Can I do this on the PS3 as well?

Edit: Thank you logo1664. It does work with certain DVD and Blu Rays. Thanks for the help.