Attain matrix transpose by row swaps and column swaps

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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@PatrickDaSilva Right, I agree. – Marc van Leeuwen Feb 18 '15 at 9:52

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?