The inverse of a matrix \( A \) is given by \( A^{-1} = \frac{1}{\text{det}(A)} \text{adj}(A) \). First, we need to calculate the determinant of the matrix \( A = \left[\begin{array}{rrr}1 & 0 & 2 \\ -1 & 2 & 3 \\ 1 & -1 & 0\end{array}\right] \).
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