How do I do this??

If there exists a matrix $\mathbf{A}$ such that $\mathbf{A} \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}, \mathbf{A} \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} -3 \\ 4 \\ 0 \end{pmatrix}, \mathbf{A} \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} -2 \\ 6 \\ 3 \end{pmatrix}$ 

calculate $\mathbf{A} \begin{pmatrix} 1 \\ -1 \\ -1 \end{pmatrix}.$

I dont know how to start this problem, any hints? Thanks!