Chapter 2, Problem 114CE

(a) Determine the Lorentz transformation matrix giving position and time in frame $S\text{'}$ from those in frame S for the case $v=0.5c$ . (b) If frame $S^{"}$ moves at 0.5c relative to frame $S\text{'}$ , the Lorentz transformation matrix is the same as the previous one. Find the product of the two matrices, which gives $x^{"}$ and $t^{"}$ from x and t. (c)To what single speed does the transformation correspond?
Explain this result.