The question is not applicable or meaningful. Decomposition is not something that is needed to display a PDF, so it is not done. The matrix is a mathematical specification of transformation, nothing more.
If you choose to take the matrix and present it to a user as separate transformations, that's up to you. You can choose to define an ordering for these transformations: it's up to you.
However, if you choose to extract an image, most people ignore the transformations. What would a scale mean? Nothing. Yes, you could honour a simple rotation or mirroring, but what effect could a skew have on a raster format?
The alternative is to extract a rendered page with everything transformed.