Altogether, two different orderings of two boosts means there are two inequivalent transformations. Each of these can be split into a boost then rotation, or a rotation then boost, doubling the number of inequivalent transformations to four. The inverse transformations are equally important; they provide information about what the other observer perceives. In all, there are eight transformations to consider, just for the problem of two Lorentz boosts. In summary, with subsequent operations acting on the left, they are