matrices - Sufficient condition for the inverse of a matrix

Let $A$ be a square matrix. Another square matrix $B$ is called inverse of $A$ if $$AB=BA=I.$$ My question is whether just $AB=I$ or $BA=I$ is not sufficient to call $B$ as the inverse of $A$? If it is not, then give a counter example where $AB=I$, but $AB\ne BA.$