If x(x - 3) = -1, then the value of x3(x3 - 18) is?

Answer: Option A

$$\begin{array}{rl}& x\left(x-3\right)=-1\\ & \Rightarrow \left(x-3\right)=\frac{-1}{x}\\ & \text{Taking cube on both sides}\\ & \Rightarrow {\left(x-3\right)}^3={\left(\frac{-1}{x}\right)}^3\\ & \Rightarrow x^3-27-9.x.\left(x-3\right)=\frac{-1}{x^3}\\ & \Rightarrow x^3-27-9\times -1=\frac{-1}{x^3}\\ & \Rightarrow x^3-27+9=\frac{-1}{x^3}\\ & \Rightarrow x^3-18=\frac{-1}{x^3}\\ & \Rightarrow x^3\left(x^3-18\right)=-1\end{array}$$