WBJEE · Maths · Determinants
If one of the cube roots of 1 be \(\omega\), then
\(\left|\begin{array}{ccc}1 & 1+\omega^2 & \omega^2 \\ 1-i & -1 & \omega^2-1 \\ -i & -1+\omega & -1\end{array}\right|=\)
- A \(\omega\)
- B 1
- C 1
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
Hints: \(\mathrm{C}_2 \rightarrow \mathrm{C}_2-\mathrm{C}_3\) \(\begin{aligned} & \mathrm{C}_3 \rightarrow \mathrm{C}_3+\mathrm{C}_2 \\ & \mathrm{C}_3 \rightarrow \mathrm{C}_3+\omega \mathrm{C}_1 \\ & \mathrm{C}_2 \rightarrow \mathrm{C}_2-\mathrm{C}_1 \end{aligned}\)
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