I am curious why $(-1)\vec{u}=-\vec{u}$ for every vector space. Since vector spaces can be defined differently, with different scalar multiplication rules, why do we have that= $(-1)\vec{u}=-\vec{u}$ is true for all vector spaces automatically? I'm missing a subtlety here! Thanks in advance!
2026-03-27 13:18:55.1774617535
Why in every vector space are the vectors $(-1)\vec{u}=-\vec{u}$?
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