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 says that this "follows from the theory of matrices". 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 45 years ago.
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