If a point $P^T=(X,Y,Z) $ is rotated by a rotation matrix R and if one of the entry of $RP$ is 0, that is $P’=RP=(0,X’,Y’)$ then what can be said about atleast one of the row of R.
I started with the elementary rotation matrix $R_x$ (X axis as the axis of rotation) and then we can generalise it to any rotation matrix . And if the point to be rotated is $(0,a,b)$ then we can’t say anything about the $R_x$. I don’t know then?