Let $S$ be a linear transformation from ${\mathbb R}^3$ to ${\mathbb R}^2$ with associated matrix $$A = \left[\begin{array}{ccc} -2 &1 &-2\cr 2 &3 &0 \end{array}\right].$$ Let $T$ be a linear transformation from ${\mathbb R}^2$ to ${\mathbb R}^2$ with associated matrix $$B = \left[\begin{array}{cc} -2 &2\cr -1 &1 \end{array}\right].$$ Determine the matrix $C$ of the composition $T\circ S$.

$C =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$