If α , β , γ are the cube roots of unity, then the value of the determinant | beginmatrix eα e2α (e3α -1) eβ e2β (e2β -1) eγ e2γ (e3γ -1) endmatrix | is equal to

Question

If α , β , &gamma; are the cube roots of unity, then the value of the determinant | beginmatrix eα e2α (e3α -1) eβ e2β (e2β -1) e&gamma; e2&gamma; (e3&gamma; -1) endmatrix | is equal to (A)  -2  (B)  -1  (C) 0 (D) 1

Tardigrade Admin · Accepted Answer

Q. If $α, β, γ$ are the cube roots of unity, then the value of the determinant $∣ ∣ e^{α} e^{β} e^{γ} e^{2 α} e^{2 β} e^{2 γ} (e^{3 α} - 1) (e^{2 β} - 1) (e^{3 γ} - 1) ∣ ∣$ is equal to

$- 2$

$- 1$

0

1

2

Q. If α,β,γ are the cube roots of unity, then the value of the determinant ∣∣​eαeβeγ​e2αe2βe2γ​(e3α−1)(e2β−1)(e3γ−1)​∣∣​ is equal to

−2

−1

0

1

2

Q. If $α, β, γ$ are the cube roots of unity, then the value of the determinant $∣ ∣ e^{α} e^{β} e^{γ} e^{2 α} e^{2 β} e^{2 γ} (e^{3 α} - 1) (e^{2 β} - 1) (e^{3 γ} - 1) ∣ ∣$ is equal to

$- 2$

$- 1$