Let $f : \mathbb{R}^{2} \to \mathbb{R}^{2}$ be the linear transformation defined by $f(x,y) = \langle -3x+y, -3x+3y \rangle$.

1. Find the matrix of the linear transformation $f$.
   
   $f(x,y) =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\displaystyle \left\lbrack \begin{array}{c} x \\ y \end{array} \right\rbrack.$
   
   
2. The linear transformation $f$ is
   injective
   surjective
   bijective
   none of these
   
   
3. If $f$ is bijective, find the matrix of its inverse. If $f$ is not bijective, enter DNE in every answer blank.
   
   $f^{-1}(x,y) =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\displaystyle \left\lbrack \begin{array}{c} x \\ y \end{array} \right\rbrack.$