I tried to prove this theorem but having hard time to start with. What I have gotten hint is that starting with rigid motion f = La(left multiplication by A) where A is in O(3) (set of all orthogonal matrices) with det(A)=-1 then using eigenvalue.
2026-02-22 21:32:54.1771795974
Prove that every proper rigid motion in space (R^3) that fixes the origin is a rotation about some axis
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What is a "proper" rigid motion? The map taking $x$ to $-x$ is a rigid motion that fixes the origin, but is not a rotation.