MatricesHard
Question
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 ω2. Then the number of distinct matrices in the set S is
, where each of a, b, and c is either ω or ω2. Then the number of distinct matrices in the set S isOptions
A.2
B.6
C.4
D.8
Solution
For being non-singular
≠ 0 ⇒ acω2 - (a + c) ω + 1 ≠ 0
Hence number of possible triplets of (a, b, c) is 2.
i.e.(ω, ω2, ω) and (ω, ω, ω).
≠ 0 ⇒ acω2 - (a + c) ω + 1 ≠ 0Hence number of possible triplets of (a, b, c) is 2.
i.e.(ω, ω2, ω) and (ω, ω, ω).
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