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please prove the given relation using determinant operations.....

mycroft holmes
272 Points
4 years ago
The given determinant can be written as

$\begin{vmatrix} b & c & a\\ c & a & b\\ a & b & c \end{vmatrix} \times \begin{vmatrix} c & a & b\\ b & c & a\\ -a & -b & -c \end{vmatrix}$

both of which are easily proved as equal to $3abc-a^3-b^3-c^3$

Hence given determinant equals $(a^3+b^3+c^3-3abc)^2$
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