Question

If $a, b, c$ are cube roots of unity, then \[ \begin{vmatrix} e^a & e^{2a} & e^{3a}-1 e^b & e^{2b} & e^{3b}-1 e^c & e^{2c} & e^{3c}-1 \end{vmatrix} \] is equal to

• A. $0$
• B. $e$
• C. $e^2$
• D. $e^3$

Hint:

For cube roots, always use $1+\omega+\omega^2=0$ and $\omega^3=1$.

Answer 1

The Correct Option is B