JEE Math Practice Question

Suppose the vectors x1, x2 and x3 are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b1, b2 and b3 respectively. if $${x_1} = \left[ {\begin{matrix} 1 \\ 1 \\ 1 \\ \end{matrix} } \right]$$, $${x_2} = \left[ {\begin{matrix} 0 \\ 2 \\ 1 \\ \end{matrix} } \right]$$, $${x_3} = \left[ {\begin{matrix} 0 \\ 0 \\ 1 \\ \end{matrix} } \right]$$ $${b_1} = \left[ {\begin{matrix} 1 \\ 0 \\ 0 \\ \end{matrix} } \right]$$, $${b_2} = \left[ {\begin{matrix} 0 \\ 2 \\ 0 \\ \end{matrix} } \right]$$ and $${b_3} = \left[ {\begin{matrix} 0 \\ 0 \\ 2 \\ \end{matrix} } \right]$$, then the determinant of A is equal to :

1. A.$${3 \over 2}$$
2. B.4
3. C.2
4. D.$${1 \over 2}$$