Two-parameter nonstandard deformation of $2×2$ matrices

We introduce a two-parameter deformation of $2×2$ matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang–Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup $GLp,q(1|1)$ by a transformation.