Let $B_1 = \{(1, 0), (0, 1)\}$ and $B_2 = \{(2, 1), (1, -1)\}$ be two bases for $\mathbb{R}^2$. If $P = \begin{pmatrix} 2 & 1 \\ 1 & -1 \end{pmatrix}$ is the change-of-basis matrix from $B_2$ to $B_1$, and $[\mathbf{v}]_{B_2} = (3, 2)^T$, what is $[\mathbf{v}]_{B_1}$?