Ques. -6

Algebra Level 3

$\left | \begin{array}{ccc} e^a & e^{2a} & (e^{3a}-1) \\ e^b & e^{2b} & (e^{3b}-1) \\ e^c & e^{2c} & (e^{3c}-1) \\ \end{array} \right |$

if $a,b$ and $c$ are cube roots of unity, find the determinant of the matrix above.