Writing a program to swap rows and columns

Swapping rows

Code.

swapRows[matrix_?SquareMatrixQ] /; EvenQ[Length[matrix]] := 
     Module[{mat = matrix, r = Range[2, Length[matrix] - 1]}, 
         mat[[r]] = mat[[Flatten[Reverse /@ Partition[r, 2]]]];
         mat
     ];

Usage.

mat = Partition[Range[36], 6];
mat // MatrixForm

swapRows[mat] // MatrixForm

Swapping columns

Code.

swapColumns[matrix_?SquareMatrixQ] /; EvenQ[Length[matrix]] := 
     Module[{mat = matrix, r = Range[2, Length[matrix] - 1]}, 
         mat[[All, r]] = mat[[All, Flatten[Reverse /@ Partition[r, 2]]]];
         mat
     ];

Usage.

swapColumns[mat]

Comments

For other swappings, you will need to generate the list of rows or columns you want to swap in the appropriate way, as mentioned by C.E. in his comment.

The Do loop comes to mind:

swapR[mat_] := Block[{mat1},
  mat1 = ConstantArray[0, Length@mat];
  Do[
   mat1[[1]] = mat[[1]];
   mat1[[Length@mat]] = mat[[Length@mat]];
   mat1[[{i, i + 1}]] = mat[[{i + 1, i}]];,
   {i, 2, Length@mat - 2, 2}
   ];
  mat1
  ]

swapC[mat_] := Block[{mat1, matT = Transpose@mat},
  mat1 = ConstantArray[0, Length@mat];
  Do[
   mat1[[1]] = matT[[1]];
   mat1[[Length@matT]] = matT[[Length@matT]];
   mat1[[{i, i + 1}]] = matT[[{i + 1, i}]];,
   {i, 2, Length@matT - 2, 2}
   ];
  Transpose@mat1
  ]

The idea of swapR is to define a new matrix, mat1, with its first and last rows the same as the input matrix mat. The other rows are interchanged pairwise with the line mat1[[{i, i + 1}]] = mat[[{i + 1, i}]] - this swaps row i and i+1. An (un-tested in the code) assumptions is that there is an even number of rows, so it has to go through i = 2, 4, ..., hence the iterator of the Do loop.

Swapping columns is equivalent to swapping rows of a transposed matrix and transposing the result, hence the Transpose in inserted in the swapC code.

The RepeatedTimings are practically the same as with Xavier's approach.

---

EDIT: The above codes answer explicitly the OP. A more flexible approach will be as follows.

To swap any two rows i and j of a general $m\times n$ matrix:

swapRij[mat_, {i_, j_}] := Block[{mat1 = mat},
  mat1[[{i, j}]] = mat[[{j, i}]];
  mat1
  ]

Usage: swapRij[mat, {1, 2}] swaps the first and second rows of mat. Note the second argument is a list.

Similarly, to swap any two columns i and j:

swapCij[mat_, {i_, j_}] := Block[{matT = Transpose@mat},
  matT[[{i, j}]] = matT[[{j, i}]];
  Transpose@matT
  ]

The functions swapRij and swapCij can be used on a set of pairs of rows/columns to be swapped. Let's take e.g. mat = Partition[Range[36], 6] and do

Fold[swapRij[#1, #2] &, mat, {{1, 2}, {3, 4}, {5, 6}}]

swaps the 1st and 2nd, 3rd and 4th, and 5th and 6th rows:

Similarly for Folding swapCij.