How to correctly get IBM from the TRS joint transformation matrix?

Question

3D

Hello!
I am writing a custom 3D graphics converter from a specific format to glTF. When exporting skinning, I ran into the problem of getting inverseBindMatrices for skeleton joints.
The input has a 4x4 matrix for each joint. When decomposing the matrix to TRS, I get valid vector3 for moving, vector4 quaternion for rotation and vector3 for scaling, the skeleton looks correct in blender after export, TRS animation also works correctly. At the same time, the mesh is turned inside out, because. there is not enough inverse matrix for local transformations.
I just can't figure out how to get the IBM matrix correctly, having a TRS matrix as input. I tried the conversion options from world to local and vice versa, as well as according to the formula proposed by the official glTF specification, but to no avail.

Answer 1

Question removed.
The solution is to convert all matrices to the world frame by multiplying by the matrix of the parent joint, then invert.