Question

If $\left| \begin{matrix} \alpha & - \beta & 0 \\ 0 & \alpha & \beta \\ \beta & 0 & \alpha \end{matrix} \right|$ = 0, then

• A. α/β is one of the cube roots of unity
• B. α is one of the cube roots of unity
• C. β is one of the cube roots of unity
• D. None of these

Answer 1

Answer: (A)

α/β is one of the cube roots of unity

Answer 2

α³ – β³ = 0

$\left( \frac{\alpha}{\beta} \right)^{3}$= 1 ⇒ $\frac{\alpha}{\beta}$ = (1)^1/3