negation - agreement with so and neither

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
or
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
or
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?

Answer

There are only a few markers in English which make a question a "negative-polarity" question:

• No


• Not



• Nothing


• Never

And any of their combined/contracted forms ("cannot", "don't", wasn't", etc.)

If and only if any of these appear in the sentence, it is considered a negative-polarity sentence and the "agreeing" response uses "neither":

• I had no idea.


• I was not present at the time.


• I had nothing to do with it.



• I never heard any complaints.

agreeing reply = Me neither!

A prefix on a word which reverses its meaning, even "non-", does not convert the sentence to negative polarity:

He was very non-committal.
- So was she.