[Math] Standard matrix of Rotation and Reflection

Question

I have been fuzzy on this transformation stuff and am practicing for an upcoming test.

 Find the standard matrix: counterclockwise rotation through 60 degrees, followed by a reflection in the line y=x

I am not exactly sure how to do this. My textbook gives an example of how to find the standard matrix of a rotation by a formula. I also know that the standard matrix of a reflection of the line y=x is {{0,1},{1,0}}. But, I don't really know how to tackle this problem.

Thanks

Answer 1

Hint: The column vectors of the linear transformation matrix will be wherever the standard basis vectors are mapped to.