3d interaction system problem: How can I achieve houdini scaling effect

In Houdini, if we rotate the object by a certain angle and then scale it along the world coordinate system, we will get the following effect: houdini scale after rotate effect. When I look at the transformation matrix, I find that as I scale the object, the changes of the three variables shear, scale and rotate will be triggered: transformation matrix. Now I'm developing an interactive system of special effects software, and I want to reproduce this interactive effect of Houdini, but I don't know how these variables are related. What should I do?