Notes for AKT-140228/0:41:45

$(A^{g})^{h}=A^{(gh)}$ ?

${\begin{aligned}(A^{g})^{h}&=h^{-1}(g^{-1}Ag+g^{-1}\mathrm {d} g)h+h^{-1}\mathrm {d} h\\&=(gh)^{-1}A(gh)+(gh)^{-1}\mathrm {d} (gh)+h^{-1}\mathrm {d} h\\&=A^{(gh)}+h^{-1}\mathrm {d} h\end{aligned}}$