Let *J* be a non-trivial ideal of a commutative ring *A*. The canonical map from *A* to the quotient *A/J* induces a homomorphism $\varphi : SL_n(A) \to SL_n(A/J)$. In general $\varphi$ is not surjective (for an example you can look here, comment 7 octobre 2010).

Question: Is there an example of non-surjectiveness using only basics known to an undergrad?