Let `omega!=1` be cube root of unity and `S` be the set of all non-singular matrices of the form `[1a bomega1comega^2theta1],w h e r e` each of `a ,b ,a n dc` is either `omegaoromega^2dot` Then the number of distinct matrices in the set `S` is a. 2 b. `6` c. `4` d. `8`

Options

A. 2
B. 6
C. 4
D. 8

Answer

A

Explanation

For being nonsingular,
`|(1,a,b),(omega,1,c),(omega^(2),omega,1)| ne 0`
or `ac omega^(2)-(a+c) omega+1 ne 0`
Hence, number of possible triplets of (a, b, c) is 2.
i.e., `(omega, omega^(2), omega)` and `(omega, omega, omega)`.