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Using the property of determinants and w...

Using the property of determinants and without expanding, prove that:`|[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0`

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Given`|[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0`
`=|[1,b c, ab+ac],[1,c a, bc+ba],[1,a b, ca+cb]|`
`C_3->C_3+C_2`
`=|[1,b c, ab+ac+bc],[1,c a, bc+ba+bc],[1,a b, ca+cb+bc]|`
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