If ω is a complex cube root of unity, then the matrix $$A=1$$ω$$2$$ωω$$2$$ω$$1$$ω$$1$$ω$$2$$ is a

Correct option is 1singular matrix

Questions

If $ω$ is a complex cube root of unity, then the matrix $A = [\begin{array}{ccc} 1 & ω^{2} & ω \\ ω^{2} & ω & 1 \\ ω & 1 & ω^{2} \end{array}]$ is a

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detailed solution

Correct option is A

We have |A|=1ω2ωω2ω1ω1ω2=1+ω2+ωω2ωω2+ω+1ω1ω+1+ω21ω2=0using C1→C1+C2+C3 and 1+ω+ω2=0∴A is a singular matrix.

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If ω is a complex cube root of unity, then the matrix A=1ω2ωω2ω1ω1ω2 is a

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If $ω$ is a complex cube root of unity, then the matrix $A = [\begin{array}{ccc} 1 & ω^{2} & ω \\ ω^{2} & ω & 1 \\ ω & 1 & ω^{2} \end{array}]$ is a