Thanks David, but in 1) I wanted to know how to look at similar matrices to the rotation matrix as well? I tried Clear[y], got the same result. I note that even when I start a new notebook, it seems to keep previous values - is there a clear all that will guarantee nothing left over from previous work? Cheers ALan

Thanks David.

1) r = RotationMatrix[theta] worked fine. If I wanted to try different matrices, for example {{Cos[theta], Sin[theta]}, {-Sin[theta], Cos[theta]}} how would I do that?

2) When I input r.{x, y} I got out[55]= {x Cos[theta] - Sqrt[1 - x^2] Sin[theta], Sqrt[1 - x^2] Cos[theta] + x Sin[theta]}

Not sure whats different?

Thanks Alan