Whether you admit it or not , India was always a distinct geographical entity even though it was always divided in many states. When invaders from central asia, iran, arabia crossed river indus they always assumed that they are entering into Hind, the land of hindus despite of its diversity. Same thing can be explained with example of turkistan, no country with such name has ever existed in the history but we use it for central asia which was always divided into numerous states.
Muslims didnt make india richer, it was always rich because of its rich fertile lands and agriculture, all muslim rulers did was to enforce taxes on local people and build beautiful buildings from it.