Inspiration and Biblical Authorship

Do i take the books of the Bible to be inspired, inerrant, and authoritative because of a prior belief about their authorship?

It seems fairly intuitive that if an apostle wrote something down, his words bear authoritative weight. If i lived in the first century, wouldn't i take it upon myself to listen carefully to Peter or John or Paul? If they wrote me a letter, i don't see why it'd be any different.

But what about someone like Luke? Luke was no apostle. He was a doctor. --A gentile doctor at that. He was an educated man who was the travelling companion of Paul and possibly others. It seems fairly evident that when he wrote his two volume work, he was consulting various sources (were they all written? were some oral? were some from his memory?--i have no idea which and how much). So what would lead me to believe that Luke's words should be taken as inspired and authoritative? There's nothing special about a gentile doctor who hung out with Paul is there?--something special enough to make me believe he wrote by way of the Holy Spirit? And knowing that he was probably doing real nitty-gritty historian work (checking and cross checking sources, laying out a chronology by investigation, etc.) which seems like a very *human* process, why would i think that the end product must be, in some sense, miraculous?

Don't get me wrong. i believe Luke and Acts are inspired and authoritative. Whether these works or others are inspired is not my point. My point is to examine the connection between our belief in inspiration and our belief in authorship. For instance, how solid a case can be made that Matthew, the apostle, truly authored (penned or dictated) the gospel we refer to as "Matthew"? Suppose you found out that the apostle, Matthew, did not write "Matthew." Would you no longer believe it was inspired and authoritative? Is your acceptance of this work (as an example--i could making the same point about any New Testament writer) as inspired and authoritative founded on your belief that Matthew authored it?