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In the last fifteen years, many operations of intuitionistic fuzzy sets were introduced for various applications, some algebraic properties of the intuitionistic fuzzy sets with these operation were discussed by a series of papers. We extend some related theories to intuitionistic fuzzy matrices and discussed the algebraic properties of the intuitionistic fuzzy matrices under the operations of arithmetic sum and arithmetic product. Also we studied the algebraic properties of necessity and possibility operators of the intuitionistic fuzzy matrices.