Prove that `|[1,a,bc] , [1,b,ca], [1,c,ab]|=|[1,a,a^2] , [1,b,b^2] , [ – InterviewSolution

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1.	Prove that `\|[1,a,bc] , [1,b,ca], [1,c,ab]\|=\|[1,a,a^2] , [1,b,b^2] , [1,c,c^2]\|`
Answer» Applying `R_(1) to aR_(1), R_(2) -R_(1) "and"R_(3) to cR_(3)`, we get LHS `=(1)/(abc) * \|[a, a^(2), abc], [b, b^(2), abc], [c, c^(2), abc]\| = \|[a, a^(2), 1], [b, b^(2), 1], [c, c^(2), 1]\| = \|[1, a, a^(2)], [1, b, b^(2)], [1, c, c^(2)]\|`

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