Let $A$ be an associative unital n-dimensional algebra over field $F$.
Show that if $ab=1$ for some $a,b \in A$ then $a=b^{-1}$
Let $A$ be an associative unital n-dimensional algebra over field $F$.
Show that if $ab=1$ for some $a,b \in A$ then $a=b^{-1}$