Determine whether or not the given linear transformation is invertible. If it is invertible, compute its inverse. (If the transformation is not invertible, enter IMPOSSIBLE. Use theta for θ.)

Question

Tθ:R2→R2, the reflection of the plane in the line formed by the angle θ with the positive x-axis
T−1(x) = Bx where B=?

Answer 1

I think you can get what you need here:

http://stackoverflow.com/questions/3306838/algorithm-for-reflecting-a-point-across-a-line