यदि `|{:(,1,w,w^(2)),(,w,w^(2),1),(,w^(2),1,w):}|=lambdaw` का `lambda` का मान ज्ञात कीजिएः

(1-w^2+w^4)(1+w^2-w^4)

If w is a complex cube root unity then |{:(1,1+w,1+w^(2)),(1+w,1+w^(2),1),(1+w^(2),1,1+w):}|=

Evaluate |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)| , where omega is a cube root 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):}] where omega is the cube root of unit.

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

|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where omega is an imaginary cube root of unity.

IF omega is cube root of unity, then |{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}| = ………. (1,0,omega, omega^2)

If w is the imaginary cube root of unity evaluate |(1,w,w^2),(w,w^2,1),(w^2,1,w)|