Problem #$9$

Use the superposed rigid body motion definitions to show the following relationships

$($a$)C_{AB}^{+}=C_{AB}$

$($b$)U_{AB}^{+}=U_{AB}$

$($c$)R_{iB}^{+}=Q_{ij}{R}_{jB}$

$($d$)B_{ij}^{+}=Q_{im}{Q}_{jn}{B}_{mn}$ where $B=F{F}^T.$