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Using properties of determinants, prove that `|(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2`

Answer» LHS=
`=[[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]]`
`=abc[[-a,b,c],[a,-b,c],[a,b,-c]]`
`=a^2b^2c^2[[-1,1,1],[1,-1,1],[1,1,-1]]`
`=a^2b^2c^2(2)[[1,-1],[1,1]]`
`=2a^2b^2c^2(1-(-1))`
`4a^2b^2c^2=RHS.


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