Generators of $SL_3(\Bbb Z)$? We know $SL_2(\Bbb Z)$ has two generators $\begin{bmatrix}1&1\\0&1\end{bmatrix}$ and $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$.
What are the generators of $SL_3(\Bbb Z)$?

The group $SL_3(\mathbb{Z})$ has a finite presentation given by 
$$ {\rm SL}(3,\mathbb{Z}) \cong \left< x, y, z \ | \ x^3 = y^3 = z^2 = (xz)^3 = (yz)^3 = (x^{-1}zxy)^2 = (y^{-1}zyx)^2 = (xy)^6 = 1 \right>
$$
  on the generators
$$
    x \ = \
    \left(
      \begin{array}{rrr}
        1 &  0 &  1 \\\
        0 & -1 & -1 \\\
        0 &  1 &  0
      \end{array}
    \right), \ \
    y \ = \
    \left(
      \begin{array}{rrr}
        0 &  1 &  0 \\\
        0 &  0 &  1 \\\
        1 &  0 &  0
      \end{array}
    \right), \ \
    z \ = \
    \left(
      \begin{array}{rrr}
        0 &  1 &  0 \\\
        1 &  0 &  0 \\\
       -1 & -1 & -1
      \end{array}
    \right).
  $$
Reference:  Marston Conder, Edmund Robertson, Peter Williams:
  Presentations for 3-dimensional special linear groups over integer rings,
  Proc. Amer. Math. Soc. 115 (1992), no. 1, 19-26.
