orthogonality – Mirror reflection and orthogonal transformation


I know a orthogonal transformation can be represented by the product of a series of mirror reflections.

But I meet a question which requires one to show that the number of the mirror reflections in the product can be no greater than $n$, the dimension of the linear space, where $nge2$.

I want to use mathematical induction to solve this question, but I got stuck on processing the situation with $n=2$, that is, a orthogonal transformation on a linear space with dimension $2$ can be represented by the product of one or two mirror reflection.

Can anyone give me some hints?