wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let ω1 be a cube root of unity and S be the set of all non-singular
1abω1cω2ω1
matrices of the form where each of a,b and c is either ω orω2. Then, the number of distinct matrices in the set S is

Open in App
Solution

We have,

1abω1cω2ω1

Solving that,

=1cωa(ωω2c)

=1(1cω)aω(1cω)

=(1cω)(1aω)

For non singular matrix.

c1ωanda1ω

cω2,aω2

A and c must be ωand b can be ωorω2.

Then, total matrix =2.

Hence, this is the answer.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Definition of Function
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon