The archetypes below are linear transformations of the form $\ltdefn{T}{U}{V}$ that are invertible. For each, the inverse linear transformation is given explicitly as part of the archetype's description. Verify for each linear transformation that \begin{align*} \compose{\ltinverse{T}}{T}&=I_U & \compose{T}{\ltinverse{T}}&=I_V \end{align*} Archetype R, Archetype V, Archetype W