Born in New York City, the son of Benjamin Ehrlich, Matthew Ehrlich graduated from Swainboro High School in Swainboro, GA, 1922 before attending Syracuse University in 1922-1924. He went on to study architecture at the University of Pennsylvania, where he earned a B. Arch. in 1927. He also studied with the T-Square Club in 1927-1929, earning a BAID Silver Medal in Archaeology, 1928. He was a teaching assistant in architecture at Penn in 1925-6.
Ehrlich worked in a number of Philadelphia firms: Thomas, Martin & Kirkpatrick (1925-1927), Frank E. Hahn (1927-1929), and Howe & Lescaze (1931-1934), becoming a partner in Carver, Davis, Ehrlich & Poole in 1939. From 1953 until about 1963, he was a partner in Ehrlich & Levinson. He retired in 1977. Ehrlich taught at the Philadelphia Museum School of Art as a lecturer and critic. He joined the national AIA in 1948 and was a member of the Philadelphia Chapter through 1963.