Thread: central reflections

(1) Let m and n be perpendicular lines through the origin O and let σm and σn
denote the reflections about the lines m and n. Let σO denote the central
reflection in O. Show directly, using the formulae for σm and σn, that
σnσm = σO.

σm(X)=2m-x
σnσm(x)=σn(2m-x)=2n-2m+x
σO=x

i dont see how these two are equal. Any ideas?