SOLUTION: Without expanding evaluate the following determinants | 1 w w2 | | w w2 1 | | w2 1 w

SOLUTION: Without expanding evaluate the following determinants | 1 w w2 | | w w2 1 | | w2 1 w | where w is a cube root of unity.

Question 737389: Without expanding evaluate the following determinants
| 1 w w2 |
| w w2 1 |
| w2 1 w | where w is a cube root of unity.
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!

| 1 w w2 |
| w w2 1 |
| w2 1 w | by operating r1=r1+r2+r3 & take 1+w+w2 common
1+w+w2=0 so the determinant=0
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