A novel Hopf algebra (G~r,sβ), depending on two deformation
parameters and five generators, has been constructed. This G~r,sβ
Hopf algebra might be considered as some quantisation of classical GL(2)βGL(1) group, which contains the standard GLqβ(2) quantum group
(with q=rβ1) as a Hopf subalgebra. However, we interestingly observe
that the two parameter deformed GLp,qβ(2) quantum group can also be
realised through the generators of this G~r,sβ algebra, provided
the sets of deformation parameters p,Β q and r,Β s are related to each other
in a particular fashion. Subsequently we construct the invariant noncommutative
planes associated with G~r,sβ algebra and show how the two well
known Manin planes corresponding to GLp,qβ(2) quantum group can easily be
reproduced through such construction. Finally we consider the `coloured'
extension of GLp,qβ(2) quantum group as well as corresponding Manin planes
and explore their intimate connection with the `coloured' extension of G~r,sβ Hopf structure.Comment: 24 page