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Prove the identities: |[a, b, c],[ a-b,...

Prove the identities: `|[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+b^3+c^3-3a b c`

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To prove the identity \[ \left| \begin{array}{ccc} a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b \end{array} \right| = a^3 + b^3 + c^3 - 3abc, ...
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