What is the mathematical theory behind the composition of transformations?

I have found a multiplication between two Transforms using Compose Transforms | Unreal Engine Documentation and I want to know how it works.

What is the mathematical theory behind this operation between two Transforms?

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You could install Visual Studio and double click the node. Then you can see the code…

There is a lot about this out there. Here’s a site that explains it: Spatial Transformation Matrices

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