Question

[R] = [4/5 -3/5] and [S] = [-3/5 4/5]
[-3/5 -4/5] and [4/5 3/5]
are reflection matrices. Calculate [R·S] and verify that it can be identified as the matrix of rotation. Determine the angle of the rotation.

Answer 1

well, R·S =
[-24/25,7/25]
[-7/25,/24/25]

Clearly this is a rotation matrix, for θ such that

cosθ = 24/5
sinθ = 7/25

with appropriate signs. I forget where the + and - are applied.