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Transformation Matrix, Inversion & Rotation

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I extracted the transformation matrix from an animated Alembic object A. This object is rotating around Y (amongst other things).

Then multiplied P by the inverted transformation matrix, to lock it to the origin, which is working as expected. 

Another objects, B, is supposed to be interacting with it. Therefore I applied the inverted transformation matrix to B as well. This is working fine, but unfortunately, B is now rotating around my original object A due to this matrix multiplication. 

There must be something very obvious that I'm missing....but...how do I now force B to not rotate around A?

Thanks for any suggestions!

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