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Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c...

Show that: `|(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b+b c+c a)dot`

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Given,
`|(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|`
(using `C_1 ->C_1 + C_2 + C_3)`
=`|(a+b+c,-a+b,-a+c),(a+b+c,b,-b+c),(a+b+c,-c+b,3c)|`
=`(a+b+c)|(1,-a+b,-a+c),(1,3b,-b+c),(1,-c+b,3c)|`
Now applying `R_2 -> R_2 – R_1, R_3 -> R_3 – R_1,` we get
=`(a+b+c)|(1,-a+b,-a+c),(0,2b+a,a-b),(0,-a-c,2c+a)|`
Expanding along `C_1`, we get
...
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