Without expanding show that `|[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2b^2,a b ,a+b]|=0`

Explanation

`R_1 -> a/a R_1`

`R_2 -> b/b R_2`

`R_3 -> c/c R_3 `

`1/(abc) | (ab^2c, abc, a(b+c)),(bc^2a^2 , abc, b(c+a)),(ca^2b^2, abc, c(a+b))|`

`((abc)(abc))/(abc) | (bc,1,ab + ac),(ac, 1, bc+bc),(ab, 1, ac+bc)|`

`c_1 + c_3 -> c_3`

`abc|(bc, 1, ab + bc+ac),(ac ,1,abb +bc+ac),(ab , 1, ab+bc+ac)|`

`= (ab + bc + ac)/(abc) | (bc, 1,1),(ac,1,1),(ab,1,1)|`

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