Matheson was educated at St Peter's College then the University of Adelaide.
[1] Matheson was a member of the Law Reform Committee of South Australia from 1971 to 1974.
Prior to his appointment as a judge of the Supreme Court, he had been a council member, vice-president and president of the Law Society of South Australia.
[1] Matheson was appointed to the bench of the Supreme Court of South Australia in 1979.
[2] Matheson has been a significant donor and benefactor to St Mark's College, a residential college affiliated with the Anglican Church of Australia for University students in Adelaide.