Does SO(3) preserve the cross product? – math.stackexchange.com

Does SO(3) preserve the cross product? – math.stackexchange.com

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Let $g\in SO(3)$ and $p,q\in\mathbb{R}^3$. I wondered whether it is true that $$g(p\times q)=gp\times gq$$ I am not sure how to prove this. I guess I will use at some point that the last row $g_3$ of ...

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