Evaluate :
`[ [ 1 , w^2 ] , [ w , w ] ] ``[ [ w , w^2 ] , [ 1 , w^2 ] ] `

Evaluate : ( 1 + w ) ( 1 - w^2 + w ) + w^2

Show that : ( 1 + w - w^2 ) ( w + w^2 - 1 ) ( w^2 + 1 - w ) = -8

If w is a complex cube root of unity, show that ([[1,w,w^2],[w,w^2,1],[w^2,1,w]]+[[w,w^2,1],[w^2,1,w],[w,w^2,1]])*[[1],[w],[w^2]]=[[0],[0],[0]]

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

If w is a complex cube root of unity, then the value of the determinant Delta = [(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w)] , is

Prove that |[1,w^2,w^2],[w^2,1,w],[w^2,w,1]|=-3w where w is a cube root of unity.

det[[x+w^(2),w,1w,w^(2),1+x1,x+w,w^(2)]]=0

det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]] =