A. Bruce Matthews, 56, chairman of the board of Washington Communications Group Inc., died Friday in Columbia, Ohio, after a heart attack.

Recently officer of Coaxial Communications Inc. in Columbus, he had been commuting there from Washington.

Mr. Matthews had served as financial vice president of the Communications Satellite Corporation (COMSAT) from 1965 until 1970. He played a key role in its development and growth and in establishment of the international satellite system, INTELSAT.

He left Washington in 1970 to become president of Bliss and Laughlin Industries in Oak Brook, Ill. Two years later, he joined the CNA Financial Corporation as a senior vice president in Chicago.

He returned here in 1975 to set up firm on Middle East and European financial and business activities. He had been with the Washington Communications Group, a newsletter and directory publishing firm, for the last two years.

Mr. Matthews was born in Clarkburg, W.Va. He learned a degree in business administration from Ohio University. He was a former partner in Arthur Andersen and Co., an accounting firm, coming to Washington from its Denver office.

He had been active in the Junior Achievement Foundation and had served as a trustee of the National Symphony Orchestra here.

Mr. Matthews was a member of the Metropolitan and International clubs here.

He is survived by his wife, the former Marjorie Nelson, of Washington; five sons, Alan Jr., of Bahrain, Thomas, of Hawaii, David of Casper, Wyo., and Christopher and James, both of Washington; two daughters, Jenifer Harper of Weston, Vt., and Michelle Evans of Washington; his mother, Hilma Matthews of Naples, Fla.; two brothers, Nelson, of Clarksburg, and Ezra, of Naples, and a sister Lois Critchfield of McLean.

The family suggests that expressions of sympathy be in the form of contributions to the Junion Achievement Foundation, 550 Summer St., Stamford, Conn., 16901, or a charity of one's choice.