If $R$ is a ring and $M$ be any maximal ideal with $a\notin M$, then there exists $q\in M$ and $s\in R$ such that forall $r\in R$ $r=sar+qr$
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.