# 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?