AddRow[M_,i_,j_,a_]:=
(IdentityMatrix[Length[M]]
+Array[If[#1==i&& #2==j,a,0]&,{Length[M],Length[M]}]).M;
MultiplyRow[M_,i_,a_]:=
DiagonalMatrix[Table[If[j==i,a,1],{j,1,4}]].M;
SwapRow[M_,i_,j_]:=
ReplacePart[M,{i-> Extract[M,j],j->Extract[M,i]}]

(Ab={{0,2,-6,4,-2},{2,2,-4,0,2},{-2,-1,1,3,-1},{3,2,-3,-5,-2}})//MatrixForm

SwapRow[Ab,1,2]//MatrixForm

MultiplyRow[%,1,1/2]//MatrixForm

AddRow[%,3,1,2]//MatrixForm

AddRow[%,4,1,-3]//MatrixForm

MultiplyRow[%,2,1/2]//MatrixForm

AddRow[%,3,2,-1]//MatrixForm

AddRow[%,4,2,1]//MatrixForm

AddRow[%,4,3,3]//MatrixForm

AddRow[%,2,3,-2]//MatrixForm

AddRow[%,1,2,-1]//MatrixForm