We agree with positive statements using so-too:
I have a red car.
(Sara) So does Sara
But with the negative statements we use neither-either:
I don't have a brother.
(Jhon) Neither does Jhon
So I can say that the most important thing before giving your agreement is to know whether the sentence is positive or negative and then to agree as I did in the examples above.
But these sentences let me think many times:
I have nothing to do.
(I) so do I
Neither do I
So the question is:
Should I consider the last sentence positive or negative?
Look at this sentence too:
The boy is impolite (It means that the boy is not polite)
(girl) so is the girl
Neither is the girl
I mean if there's a prefix (which changes the word to the opposite), then the sentence will be negative in meaning so either or neither is used?