A cannot be a knight, for then they would all be knaves, including A.
So, A is a knave.
That means that they are not all knaves, and so at least one of B and C is a knight.
So, if B would also be a knave, then C is a knight ... the only knight ... so B is telling the truth ... which doesn't work. So: B is a knight.
Which means that there is exactly one knight, and hence C is a knave.
So yes: A is a knave, B is a knight, and C is a knave.