How can we write examples of commutative and anticommutative matrices? I know how to write matrices A and B both nonzero but AB = 0. Similarly I want to know if there is a technique of writing anticommutative matrices and commutative matrices.
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possible duplicate? – Oct 04 '15 at 16:06
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I checked before posting. I did not find this question posted before. – Seetha Rama Raju Sanapala Oct 04 '15 at 16:10
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You want to know how to find matrices with $AB = BA$ or $AB = -BA$? And presumably not all matrices like that, just examples? I just want to make sure I understand. – pjs36 Oct 04 '15 at 16:22
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Yes. If I start with some A, do I have a way of finding B such that AB is either commutative or anticommutative? If for every A it is not possible, is there a way of starting with only A such that I will be able to find B? – Seetha Rama Raju Sanapala Oct 04 '15 at 16:25
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For example, the matrices should be of even order, if they are to be anticommutative, so to write a anticommutative matrix we should start with an even order matrix A. There may be further constraints on A and B. – Seetha Rama Raju Sanapala Oct 04 '15 at 23:58