[User 'Colin Fine' 's answer:] Note that so here [in so do I] has a different meaning from that it would have in the normal order ("I do so") - [the inverted so] means 'also', or 'as well' and it seems to me that it can have that meaning only when fronted. The fronting is clearly for emphasis, but that in itself is not enough to explain why the fronting is obligatory for that meaning.

So why's subject-auxiliary inversion necessary in such elliptical sentences? I doubt or don't understand the other answers in that question, such as this.

Footnote: Wikipedia doesn't appear to explain this necesary inversion.

[User 'Colin Fine' 's answer:] Note that so here [in so do I] has a different meaning from that it would have in the normal order ("I do so") - [the inverted so] means 'also', or 'as well' and it seems to me that it can have that meaning only when fronted. The fronting is clearly for emphasis, but that in itself is not enough to explain why the fronting is obligatory for that meaning.

So why's subject-auxiliary inversion necessary in such elliptical sentences? I doubt or don't understand the other answers in that question, such as this.

Footnote: Wikipedia doesn't appear to explain this necesary inversion.