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Let $A$ and $B$ be two $2\times2$ square matrices such that $AB=I$ Then prove that $BA=I$.

I tried to do it by defining $A$ and $B$ manually by listing the elements but calculations become tedious. Is there a short way to obtain this result?

One is only allowed to use concept of product of matrices and elementry transformations.

Rayees Ahmad
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    Perhaps the interesting question is whether there is a very simple proof for the $2 \times 2$ case. – lhf Apr 03 '16 at 11:43
  • @Ihf I was going to ask that on MSE and I am going through all of these linked posts and I am not able to find one for the $2\times 2$ case which is simple. – Bijesh K.S May 03 '17 at 19:47
  • Here the OP has mentioned the limitations of the tools with which the question has to be answered. I was going through all the other answers and it used linear independent sets, basis etc – Bijesh K.S May 03 '17 at 19:50

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