I. Auxiliary Verb (have/ can/ was/ do) (= helping) used with a main verb. (e.g. 'Have you locked the door?' 'Yes, I have.' (= I have locked the door))
a. use do/ does/ did for the present and past simple. (e.g. Do you like opinions?' 'Yes, I do.' (= I like opinions)
b. can use auxiliary verbs to deny what somebody says (= say it is not true) (e.g. You're sitting in my place.' 'No, I'm not.' (= I'm not sitting in your place)

I1. use have you?/ isn't she?/ do they? etc. to show interest in what somebody has said or to show surprise. (e.g. 'I've just seen Simon.' 'Oh, have you? How is he?'

I2. use auxiliary verbs with so and neither. (e.g. 'I'm feeling tired.' So am I.' (= I'm feeling tired too))
a. the word order after so and neither (verb before subject). (e.g. I passed the exam and so did Paul. (not so Paul did)
b. Instead of neither, you can use nor. Can also use not ... either. (e.g. 'I don't know.' 'Neither do I.' or 'Nor do I.' or 'I don't either.

I3. After some verbs you can use so when you don't want to repeat something. (e.g. 'Are those people English?' 'I think so.' (= I think they are English))
a. In the same way we say: I hope so, I guess so and I'm afraid so.
b. The usual negative forms are: I think so/ I expect so -> I don't think so/ I don't expect to (e.g. 'Is that woman American?' 'I think so./ I don't think so.')