If a,b and c are non- zero real number then prove that
`|{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0`

Explanation

Applying `R_(1)to aR_(1),R_(2)to bR_(2) " and " R_(3) to cR_(3)` we get
`Delta =(1)/(abc)|{:(ab^(2)c^(2),,abc,,ab+ac),(a^(2)bc^(2),,abc,,bc+ab),(a^(2)b^(2)c,,abc,,ac+bc):}| `
`=(a^(2)b^(2)c^(2))/(abc) |{:(bc,,1,,ab+ac),(ac,,1,,bc+ab),(ab,,1,,ac+bc):}| `
Applying `C_(1) to C_(3) +C_(1)` and taking bc+ca+ab common we get
`Detla =abc (bc+ca+ab) |{:(bc,,1,,1),(ac,,1,,1),(ab,,1,,1):}| =0`
`{:' C_(2)" and " C_(2) " are identical "]`