1. The problem asks to rewrite the expression for $x^{-1}$ given as a matrix: $$x^{-1} = \begin{pmatrix}0 & \frac{1}{3} \\ \frac{1}{2} & -\frac{1}{6}\end{pmatrix}$$ 2. This matrix is already in a simplified form representing the inverse of some matrix $x$. 3. To rewrite it clearly, we can express it as: $$x^{-1} = \begin{pmatrix}0 & \frac{1}{3} \\ \frac{1}{2} & -\frac{1}{6}\end{pmatrix}$$ 4. This means the element in the first row, first column is 0, first row, second column is $\frac{1}{3}$, second row, first column is $\frac{1}{2}$, and second row, second column is $-\frac{1}{6}$. 5. No further simplification is needed unless you want to write decimals, but fractions are preferred for exact values. Final answer: $$x^{-1} = \begin{pmatrix}0 & \frac{1}{3} \\ \frac{1}{2} & -\frac{1}{6}\end{pmatrix}$$