 Also closely related is the 2-fold covering group, Mp(2,R), a metaplectic group (thinking of SL(2,R) as a symplectic group).Another related group is SL±(2,R) the group of real 2 × 2 matrices with determinant ±1; this is more commonly used in the context of the modular group, however.SL(2,R) is the group of all linear transformations of R2 that preserve oriented area.