Vicky: I'm hungry.
Rachel: So am I.I haven't eaten anything all day.
Daniel: Neither have I. I didn't have time for breakfast.
We use so after a positive statement and neither after a negative one. I'm hungry. ~ So am
The structure is so/neither + an auxiliary + the subject.
The auxiliary is a form of be or have or a modal verb, e.g. can.
We're really busy at work. ~ So are we. Tom has gone to the match. ~ And so has Nick.
David can't drive, and neither can Melanie. The subject comes at the end. NOT We're busy. ~ So we are. In the present simple and past simple we use a form of do.
I love old cowboy films. ~ So do I. This phone doesn't work. ~ Neither does this one.
United won, and so did Rangers.
We can use nor instead of neither.
Emma isn't here tonight. Neither/Nor is Matthew
Fuente: Oxford practise grammar.