If `a , b , c` are real numbers, prove that `|a b c b c a c a b|=-(a+b+c)(c+b w+c w^2)(a+b w^2+c...

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If a, b and c are distinct and D=|[ a b c; b c a; c a b ]|, then the square of the determinant of... If a, b and c are distinct and D=|[ a b c; b c a; c a b ]|, then the square of the determinant of...