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.


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