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letA bea matrix of order mXn .Since we have traditional method to find the rank of matrix A by converting the given matrix into row reduced echelon form or column reduced echelon and normal form. Here we use another method to convert the given matrix A into an Anti –Row reduced Echelon form or Anti- Column Reduced Echelon form and the result matrix will give the rank of the matrix A so that the number of non-zero rows in corresponding method is the rank of A. And we have also introduced anAnti Normal Form to find the rank of A. In addition to this we have solved system of linear equations using anti echelon method.