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Given a matrix and the two operations row swap and column swap, how to prove the possibility or impossibility of getting the transpose via a composition of these operations?

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To transpose, don't you just swap all the rows and then all the columns? The same way a reflection by the axis $y = -x$ can be decomposed as reflexions along the $x$-axis and $y$-axis. –  Patrick Da Silva Sep 13 '12 at 8:00

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HINT: If $a$ and $b$ are in the same row of a matrix, can a row swap or a column swap put them into different rows of the new matrix?

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