The book deals with the problems regarding IFMs and IVIFMs. Three new operations viz., direct product, Kronecker product and Kronecker sum on IFMs are defined and studied some interesting properties. Some conditions are discussed for which a GIFM will be a generalized intuitionistic fuzzy nilpotent matrix. Also, by using the concept of relative pseudocomplement relation on intuitionistic fuzzy distributive lattice, the intuitionistic fuzzy eigenvalue and eigenvector of IFM A are defined. An application of GIFM in multicriteria decision making problem are presented. It is also proved that the set of IVIFMs form a semiring.