Prove that

Engineering

Mathematics

Introduction to Determinants

Question

Prove that $|\begin{array}{ccc} 1 & ω & ω^{2} \\ ω & ω^{2} & 1 \\ ω^{2} & 1 & ω \end{array}| = 0$

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Solving given determinant, we get

[1(ω³ – 1) – ω(ω² – ω²) + ω²(ω – ω⁴)] ....... as (ω³ = 1)

⇒ [(1 – 1) – ω(0) + ω²(ω – ω)]

⇒ 0 + 0 + 0

⇒ 0

Hence proved

Please subscribe our Youtube channel to unlock this solution.