Modular group $\mathrm {SL}(2,\mathbb Z)$ (reviewed)

The modular group is the group of $2\times2$ matrices with integer coefficients and determinant $1$; it is denoted by \( \mathrm{SL}(2,\mathbb{Z}) \) or \(\mathrm{SL}_2(\Z)\).

A standard set of generators for the modular group are the matrices: \[ S:=\begin{pmatrix}0&-1\\1&0\end{pmatrix}\quad\text{and}\quad T:=\begin{pmatrix}1&1\\0&1 \end{pmatrix}. \]