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This seems to be correct. The translation is not the same because there is a slight rotation in this transform. In that case, the translation does not need to be negative of the inverse transform. For a visual explanation, consider the following picture:
When expressing the location of frame_1
in the coordinates of frame_0
and vice versa, you can see that the norm will be the same, but the direction of the vector won't be. (In this case, the T vector of frame_0
expressed in frame_1
will be almost aligned with the -X1
axis, as opposed to the direction of the negative of the drawn T vector.)
Hope that helps.