1. The problem is to evaluate the determinant of the 3x3 matrix: $$\begin{bmatrix}6 & -6 & 6 \\ 2 & -6 & 0 \\ 10 & -5 & 5\end{bmatrix}$$ 2. The formula for the determinant of a 3x3 matrix $A = \begin{bmatrix}a & b & c \\ d & e & f \\ g & h & i\end{bmatrix}$ is: $$\det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ 3. Assign the matrix elements: $a=6, b=-6, c=6, d=2, e=-6, f=0, g=10, h=-5, i=5$ 4. Calculate each minor: - $ei - fh = (-6)(5) - (0)(-5) = -30 - 0 = -30$ - $di - fg = (2)(5) - (0)(10) = 10 - 0 = 10$ - $dh - eg = (2)(-5) - (-6)(10) = -10 + 60 = 50$ 5. Substitute into the determinant formula: $$\det = 6(-30) - (-6)(10) + 6(50) = -180 + 60 + 300$$ 6. Simplify: $$-180 + 60 + 300 = 180$$ 7. Therefore, the determinant of the matrix is $\boxed{180}$.