I am making an assumption here (not in front of Rhino) that the transformation matrix you refer to is a standard 4x4 transformation matrix and not some special annotation called that to confuse people. If I am wrong I heartily apologise for what I am about to say.
If the first cell in the matrix (1,1) is negative, then it may indicate mirroring. Or it may indicate rotation around the z-axis, or around the y-axis, or around an arbitrary axis (but not the x-axis). If is positive, but cell (2,2) is negative, that may be mirroring. If (1,1) is positive but (3,3) is negative, that may be mirroring. But again, each of these could be part of various rotations.
So it genuinely is more difficult than you think. @rajaa, any chance you could shed some insight here?
On a lighter note, @nscross, I suggest you build a prototype: any bolt that is mirrored will be left hand thread and the nuts won’t go on