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Question: With 1 \(\omega,\omega^{2}\) as cube roots of unity, inverse of which following matrices exists?...

With 1 ω,ω2\omega,\omega^{2} as cube roots of unity, inverse of which following matrices exists?

A

[1ωωω2]\begin{bmatrix} 1 & \omega \\ \omega & \omega^{2} \end{bmatrix}

B

[ω211ω]\begin{bmatrix} \omega^{2} & 1 \\ 1 & \omega \end{bmatrix}

C

[ωω2ω21]\begin{bmatrix} \omega & \omega^{2} \\ \omega^{2} & 1 \end{bmatrix}

D

None

Answer

None

Explanation

Solution

1 & \omega \\ \omega & \omega^{2} \end{matrix} \right| = 0,\left| \begin{matrix} \omega^{2} & 1 \\ 1 & \omega \end{matrix} \right| = 0,\left| \begin{matrix} \omega & \omega^{2} \\ \omega^{2} & 1 \end{matrix} \right| = 0$$ Hence inverse does not exist.