I find Gary Cottrell’s posts pleasantly readable and informative. He is very skilled in concentrating lots of information and ideas in small packages which makes his reading a well spent past time in my case.
Here is a fragment from his comments on the authorship of the Gospel of Matthew:
While the gospels tell us that Matthew was a hated tax collector, that very occupation would require him to be able to converse and write in both Aramaic and Greek. As with most male Jews, he would probably have some knowledge of Hebrew as well. What Papias refers to as the “oracles” (“logia” in Greek) may refer to a collection of the sayings of Jesus written by Matthew. Look at a red-letter edition of Matthew. Jesus says more in Matthew than any of the other gospels. It is also organized in sections. We have the Sermon on the Mount, many of the parables are arranged together, as with many of the miracles. It is as if Matthew is divided into sections that are topical, not chronological.
So here in summary is my position. I do believe that our gospel goes back to a Hebrew or Aramaic document written by the apostle Matthew. At the same time, at some point Matthew or someone else took this material, and I am guessing between AD 70-80 wrote in Greek the gospel we have now.