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The two parameter quantum deformation of 2x2 Grassmann matrices, Gr(2), andsupermatrices, Gr$(1| 1)$, are presented. Gr(2) whose matrix elements are allGrassmannian variables is called the superdual of the genel linear group GL(2),and Gr$(1| 1)$ whose diagonal matrix elements are Grassmannian variables iscalled the superdual of the supergroup GL$(1| 1)$ whose nondiagonal elementsare Grassmannian. Noncentral dual superdeterminant for Grassmann supermatricesbelonging to Gr$_{p,q}(1| 1)$ is constructed. As with the 2x2 quantum matrices,the relations satisfied by the matrix elements of the Grassmann matrices areexpressed in terms of an $\hat{R}$-matrix. The properties of $n$th power of aGrassmann supermatrix are given as an Appendix.Comment: 10 page

Two parameter deformation of Grassmann matrix group and supergroup