If A and B are square matrices of same order such that AB=A+B then prove that AB=BA

Asked Jul 03 '19 at 17:42

Active Jul 03 '19 at 17:44

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I tried everything to get the proof but I haven't reached a method yet..

edited Jul 03 '19 at 17:44

asked Jul 03 '19 at 17:42

Aashay agrawal

1

Can you be more specific about what you have tried? Clearly you haven't done “everything” yet because otherwise you would be done. – Matthew Leingang Jul 03 '19 at 17:43
Please see https://math.meta.stackexchange.com/questions/5020/ – Angina Seng Jul 03 '19 at 17:44
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Letting $A'=A-I, B'=B-I$ then the above means that $A'B'=I.$ So show that thus $B'A'=I.$ (Here $I$ is the identity matrix.) – Thomas Andrews Jul 03 '19 at 17:45
I tried squaring and multiplying it by A and B – Aashay agrawal Jul 03 '19 at 17:45
Thomas has given a good hint. – Matthew Leingang Jul 03 '19 at 17:46
Similar: https://math.stackexchange.com/q/2168444/9464 – Jul 03 '19 at 17:48

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