Alternating iff anticommutative away from 2

Let be vector spaces away from 2. Then a bilinear map is alternating iff it is anticommutative (i.e. antisymmetric). #m/thm/linalg

Proof

Let be alternating

hence is anticommutative.

Let be anticommutative. Then

and since is a multiplicative unit it follows .

From the proof, it is clear that only the forward implication holds for .

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