Let $B$ be the basis of ${\mathbb R}^2$ consisting of the vectors $$\left\lbrace \left[\begin{array}{c} 3\cr 2 \end{array}\right], \left[\begin{array}{c} -2\cr 5 \end{array}\right] \right\rbrace,$$
and let $C$ be the basis consisting of $$\left\lbrace \left[\begin{array}{c} 2\cr -1 \end{array}\right], \left[\begin{array}{c} -3\cr 2 \end{array}\right] \right\rbrace.$$

Find a matrix $P$ such that $[\vec{x}]_C = P [\vec{x}]_B$ for all $\vec{x}$ in ${\mathbb R}^2$.