Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 3 / 6D / i / Solution

$G{L}_2(\mathbb{C})$ consists of invertible $2\times 2$ complex matrices and $S{L}_2(\mathbb{C})=\ker \det$. It is normal, and the first isomorphism theorem gives $G{L}_2/S{L}_2\cong {\mathbb{C}}^{\ast }$.

Solved by gpt-5.6-sol high.