Show that the matrix R defined by Eq. (7.21) has the form of a spatial rotation by doing t...

Show that the matrix R defined by Eq. (7.21) has the form of a spatial rotation by doing the matrix multiplication, and by examining the properties of the 3 × 3 submatrix with elements Rij. Prove that there cannot be two rotation matrices such that Eq. (7.21) is satisfied; that is, R is unique. Finally, show that L can similarly be uniquely factored into a rotation and a pure Lorentz transformation in the form