Well, like I said, this won't get rid of all of it and you'll have potential phase issues should the A capella be mixed differently. You may also lose anything else panned center.
The premise being that two identical signals played out of phase with each other will cancel out.
Therefore, using the A capella in phase reverse and blending it to the full track will remove, all things being equal, the vocal track in the mix.
In practice, you'll find that it only partially removes the signal.
For any of this to work, you need to accurately line up the audio at sample level.
I just found this great explanation:
http://www.soundonsound.com/sos/sep04/a ... 0904-7.htm
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