If $A$ and $B$ are square matrices, and $AB=I$, then I think it is also true that $BA=I$. In fact, [this Wikipedia page](http://en.wikipedia.org/wiki/Invertible_matrix) says that this "follows from the associativity of matrix multiplication". I assume there's a nice simple one-line proof, but can't seem to find it.

Nothing exotic, here -- assume that the matrices have finite size and their elements are real numbers.

This isn't homework (if that matters to you). My last homework assignment was about 50 years ago.