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Question

Let ω1 be a cube root of unity and S be the set of all non - singular 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


Correct Answer
A
2
Your Answer
B
6
Your Answer
C
4
Your Answer
D
8

Solution

The correct option is A 2
|A|0, as non - singular
∣ ∣1abω1cω2ω1∣ ∣0
1(1cω)a(ωcω2)+b(ω2ω2)0
1cωaω+acω20
(1cω)(1aω)0
a1ω,c1ω
aω2,cω2
a=ω,c=ω and b{ω,ω2}  2 solutions

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