Although it appears first in the NT, it was written after Mark. Scholars date it from 60-100 CE. This would make it improbable but not impossible that Matthew, himself, wrote it.
Matthew is generally believed to be based on at least two sources: The Gospel of Mark and a hypothesized but entirely undiscovered document simply called “Q” (from the German quelle, meaning “source”).
Papias, said to be Bishop of Hieropolis (60-130 CE), apparently wrote that Matthew kept an account of the life and sayings of Christ. But Papias’ document has been lost. The early historian Eusebius (260-340 CE), however, mentions Papias’ book, The Sayings of the Lord Explained, which claims that Matthew wrote about Christ in Aramaic.
The Wikipedia entry sums up our current state of knowledge this way:
“Matthew” probably originated in a Jewish-Christian community in Roman Syria towards the end of the 1st century. The anonymous author probably drew on a number of sources, including the Gospel of Mark, the sayings collection known as the Q source, and material unique to his own community, as well as his own experience.¹
Regardless of who wrote it and how, Matthew tells us about the life, death and resurrection of Jesus Christ.
- What Matthew wrote and what did not? – Gary Cottrell’s overview (nomorefear.wordpress.com)
- Who Wrote the Oldest Gospel? Hint: The One Apostle Who Owned Ink and Parchment (cantuar.blogspot.com)
- Introduction To Gospel of Matthew: By Dr.WR ‘Dick’ Lockhart (chaplaingary.wordpress.com)
- Why Christ rose from the dead in four different ways (vridar.wordpress.com)
- Matthew 1:1-1 Posted By DR. WR “Dick” Lockhart (chaplaingary.wordpress.com)