The word “invert” can sound like an instruction to play something backwards. In audio editing it can instead refer to reversing the signal’s polarity: positive sample values become negative, and negative values become positive.
The Audacity Invert manual explains the operation and its use with matching signals. On an isolated track, polarity inversion is not the same operation as reversing time.
Try this only in a disposable practice project. Duplicate a short mono recording so both copies start at exactly the same position and retain equal level. Invert one copy, then play the pair together. Under those matching conditions, the signals cancel.
Change one condition
Lower the level of one copy slightly. The cancellation is no longer complete because the two signals no longer have equal magnitude. Restore the level before trying another change.
This demonstration depends on identical material and precise alignment. It does not establish that an arbitrary unwanted voice can be removed from a finished recording. A separately recorded voice is not an identical negative copy of the unwanted signal.
Write the experiment down as a relationship between two tracks. The important observation is what their combination does; hearing one inverted track alone does not tell the whole story.
Editorial illustration from this site’s image library; not documentary evidence of the example or object discussed.