1. Tentukan invers matriks $A = \begin{pmatrix} 1 & -1 & 0 \\ 0 & 1 & 2 \\ 1 & 0 & 3 \end{pmatrix}$. 2. Gunakan rumus invers matriks $A^{-1} = \frac{1}{\det(A)} \mathrm{adj}(A)$, di mana $\det(A)$ adalah determinan dan $\mathrm{adj}(A)$ adalah adjoin matriks. 3. Hitung determinan $A$: $$\det(A) = 1 \times \begin{vmatrix} 1 & 2 \\ 0 & 3 \end{vmatrix} - (-1) \times \begin{vmatrix} 0 & 2 \\ 1 & 3 \end{vmatrix} + 0 \times \begin{vmatrix} 0 & 1 \\ 1 & 0 \end{vmatrix}$$ $$= 1 \times (1 \times 3 - 0 \times 2) + 1 \times (0 \times 3 - 1 \times 2) + 0 = 3 - 2 = 1$$ 4. Karena $\det(A) = 1 \neq 0$, invers ada. 5. Hitung matriks kofaktor: - $C_{11} = \begin{vmatrix} 1 & 2 \\ 0 & 3 \end{vmatrix} = 3$ - $C_{12} = -\begin{vmatrix} 0 & 2 \\ 1 & 3 \end{vmatrix} = -(0 \times 3 - 1 \times 2) = 2$ - $C_{13} = \begin{vmatrix} 0 & 1 \\ 1 & 0 \end{vmatrix} = 0 - 1 = -1$ - $C_{21} = -\begin{vmatrix} -1 & 0 \\ 0 & 3 \end{vmatrix} = -((-1) \times 3 - 0) = 3$ - $C_{22} = \begin{vmatrix} 1 & 0 \\ 1 & 3 \end{vmatrix} = 3 - 0 = 3$ - $C_{23} = -\begin{vmatrix} 1 & -1 \\ 1 & 0 \end{vmatrix} = - (1 \times 0 - 1 \times (-1)) = -1$ - $C_{31} = \begin{vmatrix} -1 & 0 \\ 1 & 2 \end{vmatrix} = (-1) \times 2 - 1 \times 0 = -2$ - $C_{32} = -\begin{vmatrix} 1 & 0 \\ 0 & 2 \end{vmatrix} = -(1 \times 2 - 0) = -2$ - $C_{33} = \begin{vmatrix} 1 & -1 \\ 0 & 1 \end{vmatrix} = 1 \times 1 - 0 = 1$ 6. Matriks kofaktor: $$\mathrm{Cof}(A) = \begin{pmatrix} 3 & 2 & -1 \\ 3 & 3 & -1 \\ -2 & -2 & 1 \end{pmatrix}$$ 7. Matriks adjoin adalah transpose dari kofaktor: $$\mathrm{adj}(A) = \begin{pmatrix} 3 & 3 & -2 \\ 2 & 3 & -2 \\ -1 & -1 & 1 \end{pmatrix}$$ 8. Maka invers matriks $A$ adalah: $$A^{-1} = \frac{1}{1} \times \mathrm{adj}(A) = \begin{pmatrix} 3 & 3 & -2 \\ 2 & 3 & -2 \\ -1 & -1 & 1 \end{pmatrix}$$ Jadi, invers matriks $A$ adalah $\boxed{\begin{pmatrix} 3 & 3 & -2 \\ 2 & 3 & -2 \\ -1 & -1 & 1 \end{pmatrix}}$.