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Q.

Let ω≠1 be a cube root of unity and S be the set of all non-singular matrices of the form A=1abω1cω2ω1where a, b, c are either ω or ω2. Then number of distinct matrices in the set S is

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a

2

b

6

c

4

d

8

answer is A.

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Detailed Solution

We have|A|=11cω1−aωcω21+bω1ω2ω=1−cω−aω+acω2=(1−aω)(1−cω)A is non-singular ⇔|A|≠0⇔a=c=ω.Note that b can take any value ω or ω2.Thus, there are two non-singular matrices.
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Let ω≠1 be a cube root of unity and S be the set of all non-singular matrices of the form A=1abω1cω2ω1where a, b, c are either ω or ω2. Then number of distinct matrices in the set S is