Friday, 11 March 2016

Linear algebra, construction of counter example for two rectangular matrices such that AB=I but BAneqI

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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