The F matrix is a result of the physical rotations of the anyons. As they braid between each-other, it is important to realize that the bottom two anyons—the control group—will still distinguish the state of the qubit. Thus, braiding the anyons will change which anyons are in the control group, and therefore change the basis. We evaluate the anyons by always fusing the control group (the bottom anyons) together first, so exchanging which anyons these are will rotate the system. Because these anyons are non-abelian, the order of the anyons (which ones are within the control group) will matter, and as such they will transform the system.