JEE Math Practice Question

Let A be a 3 $$\times$$ 3 real matrix such that $$A\left( {\begin{matrix} 1 \\ 1 \\ 0 \\ \end{matrix} } \right) = \left( {\begin{matrix} 1 \\ 1 \\ 0 \\ \end{matrix} } \right);A\left( {\begin{matrix} 1 \\ 0 \\ 1 \\ \end{matrix} } \right) = \left( {\begin{matrix} { - 1} \\ 0 \\ 1 \\ \end{matrix} } \right)$$ and $$A\left( {\begin{matrix} 0 \\ 0 \\ 1 \\ \end{matrix} } \right) = \left( {\begin{matrix} 1 \\ 1 \\ 2 \\ \end{matrix} } \right)$$. If $$X = {({x_1},{x_2},{x_3})^T}$$ and I is an identity matrix of order 3, then the system $$(A - 2I)X = \left( {\begin{matrix} 4 \\ 1 \\ 1 \\ \end{matrix} } \right)$$ has :

1. A.no solution
2. B.infinitely many solutions
3. C.unique solution
4. D.exactly two solutions