in or at

Either is possible.

Thanks. Which one is more common?

Both. It depends on how you view the home: as a point location or as inside vs outside.

Do they have different connotations, then? If someone teaches music at the client's home, would you prefer "operate in" or "operate at"?

Little GirlIf someone teaches music at the client's home

I would not use 'operate' at all; that is for a business.

Wouldn't teaching music on a regular basis classify as the sole trade form of business?

Little Girlouldn't teaching music on a regular basis classify as the sole trade form of business?

Not one that 'operates'. She teaches in/at her home.

I hope it is not a strict rule. You did not, by the way, answer my other question.

Little GirlI hope it is not a strict rule.

It is not a matter of rules; it is a matter of fluent usage.

Little GirlYou did not, by the way, answer my other question.

I believe I did: She teaches in/at her home.

I just refreshed my knowledge. Teaching at the client's place would classify as a sole trade, hence a business. Thus, I do not think "operate" is wrong. I think it is more of a matter of registers.

My other question was "Do they (i.e., operate AT and operate IN) have different connotations, then?"