Let omega != 1 be cube root of unity an...

Let `omega != 1` be cube root of unity and `S` be the set of all non-singular matrices of the form `[(1,a,b),(omega,1,c),(omega^2,theta,1)],` where each of `a,b, and c` is either `omega` or `omega^2.` Then the number of distinct matrices in the set `S` is (a) `2` (b) `6` (c) `4` (d) `8`

Similar Questions

Explore conceptually related problems

If omega ne 1 is a cube root of unity, then 1, omega, omega^(2)

With 1,omega,omega^(2) as cube roots of unity, inverse of which of the following matrices exists?

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If omega is a cube root of unity,then find the value of the following: (1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(8))

If omega(!=1) is a cube root of unity,then the sum of the series S=1+2 omega+3 omega^(2)+....+3n omega^(3n-1) is

If omega (ne 1) is a cube root of unity and (1 + omega^(2))^(11) = a + b omega + c omega^(2) , then (a, b, c) equals