Matthews was born in Lindsay, Ontario. He worked as an investment broker in Toronto and rose to the position of director of various companies. Matthews served as Ontario's 16th Lieutenant Governor of Ontario from 1937 to 1946. He took office during the Great Depression while Mitchell Hepburn was Premier of Ontario. Hepburn had come to office promising to show austerity by curtailing the perks and privileges of, among others, the lieutenant-governor. Chorley Park, the grand official residence of the lieutenant-governor since 1915, was closed in the first year of Matthews' term and its contents auctioned off leaving him with a suite in the legislative buildings for official functions. As a result, Matthews did less official entertaining during his term in office at Queen's Park quarters than anticipated. He instead hosted royalty and other dignitaries at his Toronto estate.
Making many visits to churches, hospitals, military, civic, and government functions in his role as Lieutenant Governor of Ontario, Matthews brought a steady dignity to his service while in office. Highlights of his tenure include the August 18, 1938, opening with US President Franklin D. Roosevelt of the Thousand Islands Bridge, connecting Ontario to New York State. Matthews was also present for the first visit to Canada by a reigning Canadian monarch, King George VI, who was accompanied by his wife, Queen Elizabeth. Matthews and Ontario Premier Mitchell Hepburn officially welcomed the King and Queen to Queen's Park, Toronto, on May 22, 1939.