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Let $G = \operatorname{SL}_2(\mathbb{Z})/\{\pm I_2\}$. Can anyone help me in proving that $T =\left[\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array}\right] / \{\pm I_2\}$ and $S = \left[ \begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array} \right] / \{\pm I_2\}$ generates $G$.

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    Read here http://math.stackexchange.com/questions/5333/on-the-generators-of-the-modular-group , including links there. Very clear exposition.2012-05-18

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