We have a matrix $A$ of order $m$ by $n$ and a matrix $B$ of order $n$ by $m$ where entries are from real numbers. We are given that $AB =I$ and we need to check whether $BA =I$ or not. If we have square matrices then it is true but here are rectangular matrices. I know that it doesn't hold true for rectangular matrices and I am trying hard to find some counter example but unable to find such matrix. I want to learn about how to construct matrices as counter examples in linear algebra as in this case. Thanks
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