| 1 a a²-bc |
| 1 b b²-ca |
| 1 c c²-ab |

solve determinant with using properties

Let  = 1aa2-bc1bb2-ca1cc2-abApplying R1 = R1 - R2 and R2 = R2 - R3, we get = 0a-ba-ba+b+c0b-cb-ca+b+c1cc2-ab = a-bb-c01a+b+c01a+b+c1cc2-ab = a-bb-ca+b+c-a+b+c = a-bb-c × 0 = 0

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