1. In 3d the product of matrix multiplication is always in world space.
2. An objects transform is a product of its target space multiplied by its reference space.
This second part is really vital to understand, (I dont think I’ve phased it myself well enough here even) But basically it means that if your transforming an object by the world, but the object is parented the difference between the object and its target space need to be multiplied by the objects local space.
I’ll try to describe this more with pics.
Charles Looker 
I am a little confused by your first point. Even if you multiply two local space matrices will result be in world space?
It would definitely be more clear with pics. I look forward to your next post.