Subject-auxiliary inversion with SO and NEITHER / NOR to express agreement

So + auxiliary + subject is added to a positive statement to express agreement, and neither/nor + auxiliary + subject is added to a negative statement for the same purpose:

I suggested that he should take the job, and so did all his friends. (his friends also suggested that he should take the job)
Everybody knows that, and so should you. (you should know that, too)
"I love South Korean films." "Really? So do I." (I also love South Korean films)
"I am not going to Andy's party tonight." "Neither/nor is Susan." (Susan isn't going either)
"My family have never been on a holiday abroad." "Neither/nor have mine." (my family haven't been either)

If we want to express disagreement, there is no inversion:

"I love South Korean films." "I don't."
"I am not going to Andy's party tonight." "Susan is."