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Question

Let w1 be a cube roots of unity and S be the set of all non-singular matrices of the form 1abω1cω2ω1 where each a, b and c is either ω or ω2. Then the number of district 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 B 2
a, b, c {w,w2}
Let A=1abω1<ω2ω1
|A|=1(a+c)ω+acω2
Now |A| will be non-zero only when a=c=w
(a,b,c)=(ω,ω,ω) or (ω,ω2,ω)
Hence, number of nm-singular matrices =2

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