As a chess problemist he specialised in the composition of directmate three-movers, a field in which he was recognised as one of the world's leading exponents.
Matthews wrote many books on economics, among which:
The Trade Cycle, Cambridge University Press, 1960
A Study in Trade-Cycle History: Economic Fluctuations in Great Britain 1833-1842, 1954
Economic Growth and Resources, Palgrave Macmillan, 1980
Economic Growth and Resources: Volume 2, Trends and Factors, Palgrave Macmillan, 1980
British Economic Growth 1856-1973 (with C. H. Feinstein and J. Odling-Smee), Clarendon Press, 1982
He also wrote two books on chess problems:
Chess Problems: Introduction to an art (with M. Lipton and J. M. Rice), 1963