R2=I - reflecting twice is the identity. So R3=R, R4=I, etc.
In particular, R2006=I as 2006 is even.
S2 is rotation by 180° about the origin. S3=S-1 is
rotation by 270° clockwise about the origin. S4=I. So
S2006=S2.
T2 is translation two units to the right; T3 is translation
three units to the right, and so on. T2006 is translation 2006 units
to the right.
R S is not the same as S R. (In fact, to get from one to the other you
could rotate by 180° about the origin - but this isn't a surprise,
as to get from the image of R S to the image of S R we'd do S-1R-1
(the inverse of R S) followed by S R, i.e., (S-1R-1)(S R) = S-1(R-1S R)=S-1S-1=S-2=S2. However, the relationship
R-1S R=S-1 isn't introduced until the 3 star problem!).
R T2 is not the same as T2 R.
(R T)S is not the same as S(R T).
However, changing the order does sometimes produce the same transformation:
R S2=S2 R, for example. (Of course, I commutes with everything!)
The inverse of R S is (R S)-1=S-1R-1.
(S T)-1=T-1S-1.
(T R)-1=R-1T-1.
(R S2)-1=S-2R-1.