I don't entirely understand why they're framing rotations as so complex, outside of a play on words that I don't think they're making. Most rotations just use quaternions which are relatively simple. Their example of robotics uses quaternions and getting the inverse of any rotation is trivial - you literally just flip the signs of the 3 imaginary components of quaternions. For non-unit quaternions, you just then just renormalize the result (divide by the sum of the squares of the components).
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