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In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index $ m $. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.
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