Question

If $\left| \begin{matrix} a & b & 0 \\ 0 & a & b \\ b & 0 & a \end{matrix} \right|$ = 0. Then

• A. A is one of the cube roots of unity
• B. B is a one of the cube roots of unity
• C. $\left( \frac{a}{b} \right)$is one of the cube roots of unity
• D. $\left( \frac{a}{b} \right)$is one the cube roots of – 1

Answer 1

Answer: (D)

$\left( \frac{a}{b} \right)$is one the cube roots of – 1

Answer 2

∆ = a³ + b³ = 0 ⇒ a³ = – b³ ⇒ (a/b)³ = –1