2.2.1

The generated group consists of $$A = \begin{bmatrix} 1 & 1 \\ -1 & 0 \\ \end{bmatrix},\ A^2 = \begin{bmatrix} 0 & 1 \\ -1 & -1 \\ \end{bmatrix},\ A^3 = \begin{bmatrix} -1 & 0 \\ 0 & -1 \\ \end{bmatrix},\ $$

$$ A^4 = \begin{bmatrix} -1 & -1 \\ 1 & 0 \\ \end{bmatrix},\ A^5 = \begin{bmatrix} 0 & -1 \\ 1 & 1 \\ \end{bmatrix},\ A^6 = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}. $$