Question

Using properties of determinant show that: `|[1 , a , -bc] , [1 , b , -ca] , [1 , c , -a b]|=(a-b)(b-c)(c-a)`

Answer 1

`|(1,a,-bc),(1,b,-ca),(1,c,-ab)| `
`R_1 -> R_1 - R_2`
`|(0,a-b,c(a-b)), (1,b,-ca),(1,c,-ab)|`
`R_2 -> R_2 - R_3`
`|(0,a-b, c(a-b)),(0,b-c, a(b-c)),(1,c,-ab)|`
`(a-b)(b-c)|(0,1,c),(0,1,a),(1,c,-ab)|`
`(a-b)(b-c)(a-c)`
Answer