K-group, first (Ex)

Show for a commutative ring $R$$<wikitex>; Show for a commutative ring $R$ that the determinant induces an epimorphism $$\textup{det} \colon K_1(R) \to R^{\times}.$$ </wikitex> == References== {{#RefList:}} [[Category:Exercises]] [[Category:Exercises with solution]]R$ that the determinant induces an epimorphism

$\displaystyle \textup{det} \colon K_1(R) \to R^{\times}.$ $$\displaystyle \textup{det} \colon K_1(R) \to R^{\times}.$$