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 )

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.

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In note section its "then" instead of "the" before 1+w+w2(misprinting).don't be confuse.

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