Let's denote $C$ the DCT matrix and $A$ a rotation matrix (dimension is $n \times n$). The DCT of matrix $A$ is computed as follows: $$CAC^{T}$$
C is an orthogonal matrix, thus the DCT of $A$ is still a rotation matrix. Simply put, what the DCT does is compressing the information contained in a matrix. What I don't get is an interpretation of what it does to a rotation matrix, and how it 'compresses' it. It still remains a rotation matrix, but then what does it really change ? And what does the IDCT do as well then ?