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CGP EDU Academic Team
Published on: August 14, 2026
Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form, 
where each of a, b and c is either ω or ω 2 . Then the number of distinct matrices in the set S is
Text Solution
Verified by ExpertsThe correct answer is:
A
Sol. a, b, c ∈ { ω , ω 2 }
Let A = 
⇒ |A| = 1 – (a + c) ω + ac ω 2
Now |A| will be non-zero only when a = c = ω
∴ (a, b, c) ≡ ( ω , ω , ω ) or ( ω , ω 2 , ω )
∴ number of non singular matrices = 2
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