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Translation and rotation when converting from left-handed to right-handed system

I have a file with some scene information (what model to load and its transformation matrix). In Blender, I programmatically load this using python. The matrices assume a forward of -Z and an up of Y so after extracting translation and rotation (no scale), so I swap the Y and Z and multiply -1 with the Z value because Blender is Z up. Blender uses a right-handed coordinate system and my models are GLTF which I believe is also right-handed.

Because UE uses a left-handed coordinate system, what do I do with the translation and rotation so it’s properly oriented? When I first import the GLTF model, must I first do a local rotation? I’ve tried different combinations of things and I can’t get it to look right.