" So is " means " also " and " too" [a positive statement]
When we use " So is" to make short agreements, it is followed by an inversion.
Sentence Structure : So + BE (is, am, are, was, were etc.) + Subject
{ Present Simple Tense : is - Singular Subject / am - I / are : Plural Subject }
{ Past Simple Tense : was - Singular Subject / were - Plural Subject }
e.g .
John : I am fond of Techno Dancing.
Jane : So is Peter. ( Peter = Singular Subject)
" So is Peter " comes from { " Peter is also fond of Techno Dancing" } so we use Inversion to make the sentence shorter [concise] and avoid redundancy in order to add more information .
We can also use this inversion with other auxiliary verbs
Sentence Structure : So + auxiliary (do, does, did, will etc.) + Subject
e.g. After the cinema :-
Jane : I enjoyed the movie.
John : So did I.