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if $w$ is a complex cube root of unity, than $([\begin{array}{l} 1 {w w}^{2} \\ w w^{2} 1 \\ w^{2} 1 w \end{array}] + [\begin{array}{l} w w^{2} 1 \\ w^{2} 1 w \\ w w 1 \end{array}]) [\begin{array}{l} 1 \\ w \\ w^{2} \end{array}] =$

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Correct option is C

We have 1 w w2w w2 1w2 1 w +w w2 1w2 1 ww w 11ww2 = 1 w w2w w2 1w2 1 w +w1 w w2w w2 1w2 1 w 1ww2 =1+w1 w w2w w2 1w2 1 w 1ww2 =1+w000

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if w is a complex cube root of unity, than1 w w2w w2 1w2 1 w +w w2 1w2 1 ww w 11ww2=

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Ready to Test Your Skills?

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if $w$ is a complex cube root of unity, than $([\begin{array}{l} 1 {w w}^{2} \\ w w^{2} 1 \\ w^{2} 1 w \end{array}] + [\begin{array}{l} w w^{2} 1 \\ w^{2} 1 w \\ w w 1 \end{array}]) [\begin{array}{l} 1 \\ w \\ w^{2} \end{array}] =$