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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` |
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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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