In this paper, we define an operation on the intuitionistic fuzzy matrices called the Godel implication operator as an extension to the definition of this operator in the case of ordinary fuzzy matrices due to Sanchez and Hashimoto. Using this operator, we prove several important results for intuitionistic fuzzy matrices. Particularly, some properties concerning pre-orders, sub-inverses, and regularity. We concentrate our discussion on the reflexive and transitive matrices. This studying enables us to give a largest sub-inverse and a largest generalized inverse for a reflexive and transitive intuitionistic fuzzy matrix. Also, we obtain an idempotent intuitionistic fuzzy matrix from any given one.