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

A

no solution

B

infinitely many solutions

C

unique solution

D

exactly two solutions