Is "It is you who are mistaken!" correct? [duplicate]

Solution 1:

The sentence

It is you who are mistaken

is a Cleft sentence, derived from the base sentence (shown here with focussed subject You)

You are mistaken

by the Clefting process, which extracts the focussed NP (you) to be the predicate of a dummy clause with It subject and some form of be as verb (generating It is you in this case), and then making the non-focussed rest of the original sentence into a relative clause modifying the focus NP (generating who are mistaken in this case).

Verb agreement is invariant under clefting, so if the predicate is are mistaken in the original,
it will still be are mistaken in the clefted variant.

Solution 2:

The Emperor's grammar is correct. Do not question the Emperor. "You" is second person, by definition--never third person--and is therefore conjugated with the verb form "are". I think you may be tripped up by the fact that this is a very formal construction. In everyday speech, we might expect to hear "No, you're the one who's mistaken, buddy." This is colloquial and idiomatic, plus it is grammatically correct because the verb form "is" accords with "one". But, let me emphasize, "It is you who is... " is out-and-out ungrammatical and it it sounds especially bad because it is a formal register with a glaring grammatical error.