Suppose the vectors $x_1,x_2$ and $x_3$ are the solutions of the system of linear equations, $Ax=b$ when the vector $b$ on the right side is equal to $b_1,b_2$ and $b_3$ respectively. If $x_1=\left[\begin{array}{l}1\\ 1\\ 1\end{array}\right], x_2=\left[\begin{array}{l}0\\ 2\\ 1\end{array}\right], x_3=\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right]$; $b_1=\left[\begin{array}{l}1\\ 0\\ 0\end{array}\right], b_2=\left[\begin{array}{l}0\\ 2\\ 0\end{array}\right], b_3=\left[\begin{array}{l}0\\ 0\\ 2\end{array}\right]$, then the determinant of $A$ is equal to

• A

  $4$
• Correct answer
  B

  $2$
• C

  $\frac{1}{2}$
• D

  $\frac{3}{2}$

Hence, the correct answer is option: 'B'.