What $3 \times 3$ matrix would be invariant under any rotation?
i.e. $AR=RA$, where $R$ is the rotation matrix.
2026-03-25 01:29:23.1774402163
Properties for a matrix invariant under rotation (3D)?
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Hint: See what you can extract from that condition when $R$ belongs to the set:$$\left\{\begin{pmatrix}0&1&0\\-1&0&0\\0&0&1\end{pmatrix},\begin{pmatrix}0&0&1\\0&1&0\\-1&0&0\end{pmatrix},\begin{pmatrix}1&0&0\\0&0&-1\\0&1&0\end{pmatrix}\right\}.$$