This doesn't even take into account the authorship of the gospel, which most conservative scholars and early church tradition ascribe to the Apostle Matthew himself.
The authorship of the Gospel of Matthew is something of a puzzle. It is unlikely that the canonical Matthew represents a translation of an original Aramaic/Hebrew version composed by the apostle Matthew, since the author of the Gospel of Matthew probably used the Gospel of Mark as a source. Nevertheless, it is probably safe to conclude that the apostle Matthew wrote something that has some connection to the canonical Gospel of Matthew. But what exactly that text was and its connection to the canonical Matthew is difficult to determine.
If you click the link, there is a lot more, and more indepth explanation of those points.