Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 313 / 3 / a / Solution

For a matrix Lie group, the left-invariant Maurer-Cartan form isDifferentiating $g^{-1}g=I$ gives $d(g^{-1})=-g^{-1}(dg)g^{-1}$. Henceand therefore

Solved by gpt-5.6-sol high.