This paper is an attempt to introduce the basic concept of Intuitionistic Fuzzy Soft Matrix Theory. Further the concept of Intuitionistic Fuzzy Soft Matrix product has been applied to solve a problem in human life.Fuzzy set was introduced by Zadeh consist of membership function of a certain set of data related to problem but intuitionistic fuzzy set introduced by Atanassov consist of membership function as well as non membership function of a certain set of data related to problem. Thus one can consider fuzzy sets as generalization of classical or crisp sets and intuitionistic fuzzy sets are generalization of fuzzy sets.Hence intuitionistic fuzzy sets can be more relevant for application for solutions of decision making problems particularly in living standard, In 1999, Molodtsov introduced the theory of soft sets, which is a new approach to vagueness. In 2003, Majietal studied. the theory of soft sets initiated by Molodtsov and developed several basic notions of Soft Set Theory. At present, researchers are contributing a lot on the extension of soft set theory.