Wednesday 14 December 2016

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

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

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...