2) Consider the Lorentz transformation that maps (x,t) into (x',t'), where t and x are both
in time units (so x is really x/c) and all speeds are in c units also.
a) Show that the inverse of the Lorentz transformation at v is the same as the Lorentz
transformation at -v. Why is that required?
b) Show that x^2 - t^2 = x'^2 - t'^2, i.e., that x^2 - t^2 is invariant under Lorentz transformation