I'm having a hard time trying to comprehend this. How do I even start on proving the shape?
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From your tag, I am assuming these are matrices? – Vegeta the Prince of Saiyans Sep 03 '16 at 06:57
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Yes, sorry for being vague. – KNgu Sep 03 '16 at 06:57
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Notice that you can't say anything special about each matrix. For example if $B=0$ then $A$ could be anything. – 35T41 Sep 03 '16 at 06:57
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If so, then you can show that these must commute. – Vegeta the Prince of Saiyans Sep 03 '16 at 06:58
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I've heard that a subset of commuting matrices are symmetric matrices $A,B$ s.t. $AB$ is symmetric. – Eemil Wallin Sep 03 '16 at 07:03
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1I think they're after "square" as the answer... – Arthur Sep 03 '16 at 07:04
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In this question "shape" actually means "shape", the outer form of the matrix. So you are asked about the number of rows and columns. Assuming $A$ is a $k\times l$ matrix and $B$ is a $m\times n$ matrix, what does the equation $AB=BA$ tell you about $k,l,m,n$? No question is asked about the entries of $A,B$ (what $AB=BA$ tells about them is quite complicated, but you should ignore it).
Marc van Leeuwen
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