# Special linear group:SL(2,Z)

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The group $SL(2,\mathbb{Z})$ is defined as the group, under matrix multiplication, of $2 \times 2$ matrices over $\mathbb{Z}$, the ring of integers, having determinant $1$.
$\{ \begin{pmatrix} a & b \\ c & d \\\end{pmatrix} \mid a,b,c,d \in \mathbb{Z}, ad - bc = 1 \}$