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|(bc,bc'+b'c,b'c'),(ca,ca'+c'a,c'a'),(ab...

`|(bc,bc'+b'c,b'c'),(ca,ca'+c'a,c'a'),(ab,ab'+a'b,a'b')|` is equal to

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|(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b))|=

ab(a-b)+bc(b-c)+ca(c-a) is equal to

|{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

det[[1,bc,bc(b+c)1,ca,ca(c+a)1,ab,ab(a+b)]]=0

Without expanding show that : |(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b))|=0

|[bc, b+c, 1], [ca, c+a, 1], [ab, a+b, 1]|=?