Matić was born in Bogatić, Kingdom of Yugoslavia, present-day Serbia on 8 September 1937, but moved to present-day Bosnia and Herzegovina early in his childhood. He attended elementary and high school in Visoko.[1] His subsequent education was at the University of Zagreb, where he earned a BS in 1960. He earned an MS at the University of Belgrade in 1963, and finally a PhD at the University of Sarajevo in 1971.[2] Matić was part of a large engineering team which worked on the project of the electrification of the Sarajevo–Ploče railway in the 1960s and 1970s.[2]
Following the 2000 parliamentary election, the SDP BiH formed a coalition with the Party for Bosnia and Herzegovina to gain a majority and force the nationalist parties out of power. They gathered a coalition of many other small parties to create the "Alliance for Change". Matić became Chairman of the Council of Ministers and Minister of Finance and Treasury on 22 February 2001.[4] The SDP BiH-led government facilitated the passage of the Election Law, which was not only an important step towards democracy, but also a prerequisite to Bosnia's accession to the Council of Europe.[5] He served in both offices until July 2001.[6]
Matić died on 12 May 2016 in Sarajevo, Bosnia and Herzegovina at the age of 78.[8] He was buried in Sarajevo at the Bare Cemetery on 14 May, two days after his death.[9]