I am trying to understand affine maps. In the book I am using there is the following example, which I don't understand. Given are the following points: \begin{array}{lll} p_0 = \begin{pmatrix} 1 \\ 1 \end{pmatrix}, & p_1 = \begin{pmatrix} 1 \\ 2 \end{pmatrix}, & p_2 = \begin{pmatrix} 0 \\ 1 \end{pmatrix}, \\ q_0 = \begin{pmatrix} -2 \\ -1 \end{pmatrix}, & q_1 = \begin{pmatrix} \phantom{-}0 \\ -1 \end{pmatrix}, & q_2 = \begin{pmatrix} -2 \\ -2 \end{pmatrix}. \end{array}
Then the following vectors are computed \begin{array}{ll} \overrightarrow{p_0 p_1} = \begin{pmatrix} 0 \\ 1 \end{pmatrix}, & \overrightarrow{p_0 p_2} = \begin{pmatrix} -1 \\ \phantom{-}0 \end{pmatrix}, \\ \overrightarrow{p_0 p_1} = \begin{pmatrix} 2 \\ 0 \end{pmatrix}, & \overrightarrow{p_0 p_1} = \begin{pmatrix} \phantom{-}0 \\ -1 \end{pmatrix}. \end{array}
I am asked to find an affine map such that $f(p_{i})=q_{i}$.
It now says that the matrix of the map determined by $F(\overrightarrow{p_0 p_i})=\overrightarrow{q_0 q_i}$, $i=1,2$ is given by $$ A = \begin{pmatrix} 0 & 2 \\ 1 & 0 \end{pmatrix}. $$
I don't understand how I get this matrix. I would say it is the following one, but I guess I am wrong. I did everything with repect to the bases $\{(0,1),(-1,0)\}$ and $\{(1,0),(0,1)\}$. I am not sure about the second basis, but since there is no other basis mentioned I thought it is the one the author has used too. $$ \begin{pmatrix} 2 & \phantom{-}0 \\ 0 & -1 \\ \end{pmatrix} $$
Unfortunately I don't know where I making the mistake.
I would really appreciate some help. Thanks a lot in advance!