I hope you got a clear answer.

Goes the same old rule. "ask what the matter is" is correct. "ask what is the matter" is incorrect, however, frequently heard in colloquial speech. Hands down. The adverbial (prep + noun) does not matter, put it wherever you feel like. But most common to say "ask what the matter is with you". The subject is "matter", same as in "what is your name", "(your) name" being the subject. This confuses many native speakers, the reason why "ask what's the matter" sounds natural is that, simply that, people say it often enough. It almost becomes a "fixed" idiom, so the rule is you don't make change to an idiom. There is only this one exception: Which. You could say "ask which is the answer", which'd be taken as correct, but still, "ask which the answer is" is the correct one in strict grammar. And do tell the difference between "what's good/wrong" and "what's your name/an apple", as Mr. Brown suggested yet failed to clarify.

I greatly appreciate your detailed explanation, Hurley "Hurl" the Loner .

What? Are you serious? >>> "What's it?" <<< subject: "it". >>> "Is that it?" <<< Subject: "that". Have any idea what an "inversion sentence" is? The actual order in a "what" question is, "this is what?", so "this" is the subject. Of course the subject is "something" in your example, because it's not a "what" question per se! I answered this question because both of the other 2 people just had you the wrong answers to both of your questions respectively. Superstitious, sloppy and credulous you are. Or are you trying to be funny here? You're unbelievable, man.

"he asked me what was the matter with me" is correct. The second one is OK as well but personally I would remove the 'with me'. When we we ask a question with 'the matter' it , we want to find the problem or the cause of the person's unhappiness. What's wrong? What's the matter? What's the problem?