Find det A for
A=\begin{bmatrix}0&2&0&0&0&0\\0&0&0&8&0&0\\0&0&0&0&0&2\\3&0&0&0&0&0\\0&0&0&0&5&0\\0&0&1&0&0&0\end{bmatrix}.
Only one pattern P makes a nonzero contribution toward the determinant:
Thus, \rm{det \ A = (sgn \ P)(prod \ P) }= (−1)^72 · 8 · 2 · 3 · 5 · 1 = −480.