Past exam of the mathematics course of the University of Cambridge / 2010 / ia / Paper 3 / 1D / iii / Solution

For column vectors, the second transformation multiplies on the left of the first. Thus the required matrix is $SR$, not $RS$. Using the rotation matrix convention in part (i),Indeed, a vector first becomes $(x,qy+qz,-qy+qz)$, and the orthogonal reflection then exchanges its first two entries.