`|[1,1+iota+omega^2,omega^2],[1-iota,-1,omega^2-1],[-iota,-iota+omega-1,-1]|`=
`(a) 0`
`(b) 1`
`(c) iota`
`(d) omega`

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(1-i,-1,omega^2-1),(-i,-1+omega,-1)| (A) omega (B) i (C) 1 (D) 0

|[omega+omega^(2),1,omega],[omega^(2)+1,omega^(2),1],[1+omega,omega,omega^(2)]|

If omega is a cube root of unity, then |(1-i,omega^2, -omega),(omega^2+i, omega, -i),(1-2i-omega^2, omega^2-omega,i-omega)|= (A) -1 (B) i (C) omega (D) 0

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

Find the value of (-iota)^-117 is ( A ) -1 ( B ) iota ( C ) 1

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]

If omega is a complex cube root of unity,show that ([1 omega omega^(2)omega omega^(2)1 omega^(2)1 omega]+[omega omega^(2)1 omega^(2)1 omega omega omega^(2)1])[1 omega omega^(2)]=[000]