Find all integer solutions $(a, b)$ with $a>b>0$ of the equation $a b-a-b=1$.

 untranslated text has been translated while preserving the original formatting and structure.
With the factorization of the rectangle, the equation rewrites as $(a-1)(b-1)=2$ therefore $a-1=2$ and $b-1=1$, i.e., $a=3, b=2$.