QuestionFind the inverse of $$\left[\begin{array}{ccc} 1 & -1 & 2 \\ 0 & -1 & -1 \\ 1 & 0 & 2 \end{array}\right]$$

Studdy Solution
Calculate the inverse using the formula:
$A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adjugate}(A)$
Since $\text{det}(A) = 1$, the inverse is simply the adjugate:
$A^{-1} = \begin{bmatrix} -2 & 2 & 1 \\ -1 & 0 & 0 \\ 1 & -1 & -1 \end{bmatrix}$
The inverse of the given matrix is:
$\boxed{\begin{bmatrix} -2 & 2 & 1 \\ -1 & 0 & 0 \\ 1 & -1 & -1 \end{bmatrix}}$