Special linear group:SL(2,Q)

Definition
The group $$SL(2,\mathbb{Q})$$ is defined as the group of $$2 \times 2$$ matrices with rational entries and determinant $$1$$, under matrix multiplication.

$$SL(2,\mathbb{Q}) := \left \{ \begin{pmatrix} a & b \\ c & d \\\end{pmatrix} \mid a,b,c,d \in \mathbb{Q}, ad - bc = 1 \right \}$$.

It is a particular case of a member of family::special linear group over rationals, member of family::special linear group of degree two, and hence of a member of family::special linear group.