A transformation $T: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ is defined by $T(v) = Av + b$, where $A = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$ and $b = \begin{pmatrix} 2 \\ -3 \end{pmatrix}$. Which of the following statements accurately describes this transformation?