Without expanding the determinants show that

1 w w2

w w2 1

w2 1 w

=0 where w is one of the cube roots of unity.

(w2 means w square )

Question

Without expanding the determinants show that
1 w w2
w w2 1
w2 1 w
=0 where w is one of the cube roots of unity
(w2 means w square )

Sr · Accepted Answer

apply R1--->R1+R2+R2 you will get first column as
1+w+w2 which is equal to zero
NOTE:if w is the cube root of unity the 1+w+w2 =0