inverting the instrumental over the regular will work is the beat is lined up perfectly and the instrumental track is identical to the beat on the full song version. THERE IS, one other way, although it doesn't work quite as well, you can do it without the use of the instrumental track
Ok, so you take the track, and throw it in pro tools or another audio editing software, and create 3 tracks (must use wav, mp3's wont work). Copy the song onto all 3 tracks with the exact same start point. Pan 1 left, pan 1 right, and keep one panned center. The track that's panned center, invert it. this should in theory cancel out all the frequencies that are panned dead center, which is usually always lead vocals and drums. this can be great if you dont want the drums from a sample.
To be perfectly honest, I'm not totally sure if it works as expected, I'm just paraphrasing Duro, who I work for. He's got a column in Scratch Magazine called "Ask Duro" and this was one of the questions asked. I think I have it right but I may be a little mistaken....
This question was posed to him in either the Lil Jon, or the Scratch after Lil Jon (Nas/Premo I think?). Definately around 2 or 3 issues ago.