Originally Posted by
Gamma did you type it right? that bottom 2x2 minor has rows the same, is that correct?
If so, just do it, i recommend cofactor down the first column to take advantage of that being the same.
the first term is 0.
second is
$\displaystyle -(1+w^2)[-w+w^2]$
third is
$\displaystyle (w^2+w)[-w+w^2]$
Add them
$\displaystyle (-1-w^2 +w^2 +w)[-w+w^2]=(-1+w)[-w+w^2]=1-w^2-w^2+w=-2w^2+w+1$
But these are cube roots of unity, $\displaystyle w^2+w=-1 \Rightarrow w=-1-w^2$
$\displaystyle -2w^2+w+1= -2w^2 (-1 - w^2) + 1= -3w^3=-3$