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

Explanation

`Delta= |{:(1,,ab,,(1)/(a)+(1)/(b)),(1,,bc,,(1)/(b)+(1)/(c)),(1,,ca,,(1)/(c)+(1)/(a)):}|`
`=(1)/(abc) |{:(1,,ab,,ac+bc),(1,,bc,,ab+ca),(1,,ca,,bc+ab):}| " ""(Multiplying "C_(3)" by abc)"`
`=(1)/(abc) |{:(1,,ab,,ac+bc+ab),(1,,bc,,ab+ca+bc),(1,,ca,,bc+ab+ca):}|" ""(Applying "C_(3)toC_(3) +C_(2)")"`
`=((ab+bc+ca))/(abc) |{:(1,,ab,,1),(1,,bc,,1),(1,,ca,,1):}|=0`