According to the Remington chart by Boyd Scott Remington at RIHSL, this Matthew Remington was Captain of the 1st Cranston Company in 1763. Genealogist Martha A. Benns' book "Remington Family" has this Matthew (who married Martha Randall) as a son of Thomas & Mary (Allen) Remington; a Matthew is named in Thomas's will. However, it seems more likely that the earlier Matthew married Hepsibah Blackington (please see the notes for the other Matthew, who was "of Warwick"). An online genealogy has no parents noted for this one, but has his birth date as 12 September 1724 (source noted is "Descendants of William Randall") -- needs further research.
He is possibly the Mathew Rimenton listed as a resident of Coventry in the RI 1774 census (1 WM>16, 4 WM<16, 2 WF>16, 2 WF<16); also the Matthew Remmington 16 - 50 A, listed at West Greenwich, RI, in the 1777 RI Military Census.
The 1774 census data suggests that Matthew may have had four sons (?) born before 1774 in addition to two daughhters.
If this marriage to Martha Randall is a third marriage for the "other" Matthew, s/o Thomas & Mary (Allen) Remington, then we might conclude that Peleg did not have a brother Matthew (?). Genealogists differ on this. However, a note within parentheses in the genealogy entitled "John Remington of Massachusetts" in the possession of the Roger Williams Family Association (from Mrs. Adair), says that Peleg "and his brother left home when their father married a second time." This is evidence that Peleg did have a brother.