Consider this proof of the triple product identity. In this proof, they state that $\lambda $ does not depened on any choice of three vectors $A,B,C$. I don't understand why is that true? I'll appreciate any help!
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Quick answer: Use trilinearity of the triple cross product. See this previous question – user10354138 Jul 22 '20 at 10:22
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@user10354138 what is exactly trilinearity ? – Tair Galili Jul 22 '20 at 10:23
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linear in the three variables $A$, $B$, $C$ separately. – user10354138 Jul 22 '20 at 10:28
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@user10354138 what you mean is that $(A_1+A_2)\times B\times C = A_1\times B\times C+A_2\times B\times C$, and also for $B,C$ as well – Tair Galili Jul 22 '20 at 10:30