# What is wrong with my determinant calculation?

$$\left| {\begin{array}{*{20}{c}} 2 & 6 & 4 & 0 \\ 2 & 0 & 4 & 2 \\ 0 & 3 & 2 & 1 \\ 2 & 6 & 4 & 8 \\ \end{array}} \right| = \left| {\begin{array}{*{20}{c}} 2 & 6 & 4 & 0 \\ 0 & { - 6} & 0 & 2 \\ 0 & 3 & 2 & 1 \\ 0 & 0 & 0 & 8 \\ \end{array}} \right| = 2\left| {\begin{array}{*{20}{c}} { - 6} & 0 & 2 \\ 3 & 2 & 1 \\ 0 & 0 & 8 \\ \end{array}} \right| = 2*8\left| {\begin{array}{*{20}{c}} { - 6} & 0 \\ 3 & 2 \\ \end{array}} \right| = 16*( - 12 - 0) = - 192$$

Your calculation is correct. If you haven't copied the matrix wrongly or otherwise introduced a factor of $2$, the "correct" answer is wrong. –  Daniel Fischer Jan 17 '14 at 15:46
Nothing is wrong, the correct answer is $-192$. Verification:
sage: Matrix([[2,6,4,0],[2,0,4,2],[0,3,2,1],[2,6,4,8]]).det()