As far as I am aware this is something one does for analog processing, not in digital, and one only does it during the actual processing and not in storage (for example in an mp3).
Is my thinking correct?
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Well, Audacity has an option to do that on digital files, so I assume that means it is done.
From that page:
Invert flips the audio samples upside-down, reversing their polarity. The positive samples (above the horizontal zero line in the Audacity Waveform) are moved below the zero line (so becoming negative), and negative samples are made positive. Invert does not usually affect the sound of the audio at all, but it can be used for audio cancellation. If Invert is applied to one track and that track is mixed with another uninverted track that has identical audio, the identical audio is cancelled out (silenced).
One indeed does, if mostly for text and evaluation purposes. See, for example, http://www.audiocheck.net/audiotests_polaritycheck.php