1. Diketahui matriks $$A=\begin{bmatrix}-4 & 5 & 2 \\ 0 & -2 & 4 \\ -1 & -6 & 3\end{bmatrix}$$, tentukan nilai determinan $$\det(A)$$. 2. Rumus determinan matriks 3x3 adalah: $$\det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ di mana matriks $$A=\begin{bmatrix}a & b & c \\ d & e & f \\ g & h & i\end{bmatrix}$$. 3. Substitusi nilai dari matriks $$A$$: $$a = -4, b = 5, c = 2$$ $$d = 0, e = -2, f = 4$$ $$g = -1, h = -6, i = 3$$ 4. Hitung setiap bagian: $$ei - fh = (-2)(3) - (4)(-6) = -6 + 24 = 18$$ $$di - fg = (0)(3) - (4)(-1) = 0 + 4 = 4$$ $$dh - eg = (0)(-6) - (-2)(-1) = 0 - 2 = -2$$ 5. Hitung determinan: $$\det(A) = -4 \times 18 - 5 \times 4 + 2 \times (-2) = -72 - 20 - 4 = -96$$ Jadi, nilai determinan matriks $$A$$ adalah $$-96$$.