Solve this following

If $A=\left(\begin{array}{cc}2 x & 0 \\ x & x\end{array}\right)$ and $A^{-1}=\left(\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right)$ then $x=?$

A. 1

B. 2

C. $\frac{1}{2}$

D. $-2$