When you reflect a vector with reflection matrix on 2 dimensional space, and 3 dimensional space, intuitively we know there's rotation matrix can make same result.
But is it possible on higher dimension(4, 5, 6...)?
I know rotation matrix can be represented through reflection matrix product reflection matrix, not vice versa.
If you have two vectors $u$ and $v$ with $|u|=|v|$, you can construct both a reflection and a rotation in any dimension that will transfer $u\to v$.
For reflection: take hyperplane with normal $u-v$.
For rotation: rotate in plane $(u,v)$ by angle $\arccos(u\cdot v)$ and by any other angles in orthogonal planes.
However, the result of this transformation will be the same only for vector $u$ because in general reflection is not the same as rotation.