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Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

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SOLUTION :`[[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]]`
`[[a+b,-c-b,-b],[a+b,b+c,-a],[-a-b,b+c,a+b+c]]`
`(C_1=C_1+C_2, C_2=C_2+C_3)`
=`(a+b)(b+c)[[1,-1,-b],[1,1,a],[-1,1,a+b+c]]`
`(a+b)(b+c)[[0,-1,-b],[2,1,a],[0,1,a+b+c]]`
`(C_1=C_1+C_2)`
=`(a+b)(b+c)xx(-2)[[-1,-b],[1,a+b+c]]`
=-2(a+b)(b+c)(-a-b-c+b)
=2(a+b)(b+c)(c+a)


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