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Question

Let ω1 be a cube root of unity and S be the set of all nonsingular matrices of the form 1abω1cω2ω1, where each of a, b and c is either ω or ω2. Then the number of distinct matrices in the set S is

A
2
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B
6
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C
4
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D
8
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Solution

The correct option is A 2
Let Δ=1abω1cω2ω1=1(1cω)a(ωω2c)+b(ωωω2)=(1aω)(1cω)
Δ is non singular Δ0a=c=ω
Note that b can take any vale ω or ω2
Thus there are two non singular matrices.
Hence, option 'A' is correct.

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