Gospel According to Matthew in Fausset's Bible Dictionary

frontGOSPELS for its aspect of Christ compared with the other evangelists.) Time of writing. As our Lord's words divide Acts (Acts 1:8) into its three parts, "ye shall be witnesses unto Me in Jerusalem, and all Judea, and in Samaria, and unto the uttermost part of the earth": (1) the period in which the church was Jewish, Acts 1-11; (2) the period when it was Gentile with strong Jewish admixture; (3) the period when the Gentiles preponderated, Matthew's Gospel answers to the first or Jewish period, ending about A.D. 41, and was written probably in and for Jerusalem and Judea. The expression (Matthew 27:7-8; Matthew 28:15) "unto this day" implies some interval after Christ's crucifixion. Language. Ancient testimony is unanimous that Matthew wrote in Hebrew Papias, a disciple of John (the Presbyter) and companion of Polycarp (Eusebius, H. E. 3:3), says, "Matthew wrote his oracles (logia) in Hebrew, and each interpreted them in Greek as he could." Perhaps the Greek for "oracles," logia, expresses that the Hebrew Gospel of Matthew was a collection of discourses (as logoi means) rather than a full narrative. Matthew's Gospel is the one of the four which gives most fully the discourses of our Lord. Papias' use of the past tense (aorist) implies that "each interpreting" Matthew's Hebrew was in Papias' time a thing of the past, so that as early as the end of the first century or the beginning of the second the need for each to translate the Hebrew had ceased, for an authoritative Greek translation existed...

Link: https://bible-history.com/faussets/M/Matthew,+the+gospel+according+to/