# Switching rows and columns in a matrix

Let's suppose that you have this $$4\times4$$ matrix:

$$\begin{bmatrix} 12&10&11&09\\ 16&14&15&13\\ 08&06&07&05\\ 04&02&03&01 \end{bmatrix}$$

And let's say that you can swap only $$N$$th row with $$(N+1)$$th row or $$(N-1)$$th row and Nth column with $$(N+1)$$th column and $$(N-1)$$th column.

Is it possible to swap columns and rows this way, to get "$$05$$" element from matrix to where is "$$15$$" and that everything remains the same?

(If you can find the answer, can you write it down this way: If you swap rows, say: "row $$1,2$$". That means you swap row $$1$$ with row $$2$$. If you swap columns, say:" columns $$1,2$$". That means that you swap column $$1$$ with column $$2$$)

Say that in the initial position columns have sums $$a,b,c,d$$. When you swap two columns you again have the same sums, just in a different order. Swaping rows does not impact column sums.