For of one thing he took especial care, not to omit anything he had heard, and not to put anything fictitious into the statements." This is what is related by Papias regarding Mark.
Irenaeus wrote (Against Heresies 3.1.1): "After their departure [of Peter and Paul from earth], Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter." Note that Irenaeus had read Papias, and thus Irenaeus doesn't provide any independent confirmation of the statement made by the earlier author.
It seems unlikely that This is what Christian tradition has handed down, however, and to be fair, it's a tradition that dates back pretty far — to the writings of Eusebius around the year 325.
But then the actual positive arguments for Matthaean authorship given by the same scholar (internal or external) will be omitted in the Muslim paper or not handled properly.
This method assumes that traditional authorship can’t be demonstrated apart from a statement saying “I Matthew wrote this Gospel”.
This has been called into question on innumerable points by hosts of critics; Dr. For he neither heard the Lord nor attended on Him, but afterwards, as I said, (attended on) Peter, who used to give his instructions according to what was required, but not as giving an orderly exposition of the Lord's Words.
Abbott, however, considers him "a most careful and conscientious writer." Papias's work itself has disappeared. So that Mark made no mistake in writing down some things as he recalled them.