यदि omega इकाई का घनमूल हो तो ,सारणिक `|(1,w^3,w^2),(w^3,1,w),(w^2,w,1)|` का गान ज्ञात कीजिये।

Find the value of : |(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1)|

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

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]]

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

Find the value of : |(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)|

If omega is cube root of unit, then find the value of determinant |(1,omega^3,omega^2), (omega^3,1,omega), (omega^2,omega,1)|.

Evalute: |{:(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1):}| , where omega is an imaginary cube root of unity .