1. The problem is to find the determinant of the matrix $$A = \begin{bmatrix} 2 & 4 & 1 \\ 5 & 2 & 3 \\ 1 & 4 & 8 \end{bmatrix}$$. 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: $$\det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ This formula expands the determinant along the first row. 3. Substitute the values from matrix $$A$$: $$a=2, b=4, c=1, d=5, e=2, f=3, g=1, h=4, i=8$$ 4. Calculate each minor determinant: $$ei - fh = (2)(8) - (3)(4) = 16 - 12 = 4$$ $$di - fg = (5)(8) - (3)(1) = 40 - 3 = 37$$ $$dh - eg = (5)(4) - (2)(1) = 20 - 2 = 18$$ 5. Plug these back into the determinant formula: $$\det(A) = 2 \times 4 - 4 \times 37 + 1 \times 18 = 8 - 148 + 18$$ 6. Simplify the expression: $$8 - 148 + 18 = (8 + 18) - 148 = 26 - 148 = -122$$ 7. Therefore, the determinant of matrix $$A$$ is $$\boxed{-122}$$.