I have a problem with proving this:
$\text{For} \ s(x)=\begin{cases} -1, \ -1<x<0 \\ 1, \ 0<x<1\end{cases}, \ s(x+2)=s(x), \ \text{Prove that each s(kx) (k=1,2,3,...) is orthogonal, that is,} \ \int_{-1}^1 s(ix)s(jx)dx=0 \ \text{for i}\neq\text{j}.$
How Can I prove this? I have no idea about any approaches.