Yes, the question is absolutely correct. 'A' would be wrong. It's not referring to any particular individual object, but rather to the invention :the overall concept of 'the fridge'. Alexander Graham Bell invented the telephone.

We use "the fridge" because "fridge" is specific. If it was "a fridge" it could be any fridge.

"The" is used in this sentence because it is referring to the general concept of fridges, not a specific fridge. Also, the question is correct, although it does sound more like British English rather than American English. In American English we would probably say "Do you have any idea who invented the fridge?".

the is used in particular cases we used it in specail cases when we want to specify some thing

Do you have any idea.. the fridhe as a class and not 'some fridge' :) Have a good day :)