I think he’s asking this, LOL.
“Using scripture alone show that Matthew wrote a gospel and that it is inspired.”
I would say that, using historical documents, you explain why and how the gospel of Matthew is accepted as the inspired Word of God. Show how one can know that Matthew wrote it and it is inspired.
The historical record is what gives Matthew its certification for being 'inspired'....? Wow with this filtration system nobody would ever get around to reading with understanding the Gospel of Matthew.