If a b 00 a bb 0 a=0 then,

If $|\begin{array}{lll} a b 0 \\ 0 a b \\ b 0 a \end{array}| = 0$ then,

A
$a$ is one of the cube roots of unity
B
$\frac{a}{2}$ is one of the cube roots of unity
C
$b$ is one of the cube roots of unity
D
$\frac{a}{b}$ is one of the cube roots of-1

Solution:

We have,

$|\begin{array}{lll} a b 0 \\ 0 a b \\ b 0 a \end{array}| = 0$

$\Rightarrow a^{3} + b^{3} = 0$

$\begin{array}{l} \Rightarrow (\frac{a}{b})^{3} = - 1 \\ \Rightarrow \frac{a}{b} is one of the cube roots of - 1 \end{array}$

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