$SL_3(\mathbb{F_2})$ is the set of all invertible $3x3$ matrices over the field $F_2$ with determinant $1$. From what I understand $F_2$ is the set $\{0, 1\}$, ie.. $\mathbb{Z}$ mod $2$.
As far as I can see then, $SL_3(\mathbb{F_2})$ has to be $I_3 = \begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1 \end{bmatrix}$
If the $1$'s were in any other location we would have zero determinant. So is this $SL_3(\mathbb{F_2})$?