A = {{2,3,-4},{1,-2,2},{-1,16,-18}};

RowReduce[A]//MatrixForm

(B = {A[[1]],A[[2]]})//MatrixForm

RowReduce[B]//MatrixForm

(CMat = {A[[3]],A[[1]]})//MatrixForm

RowReduce[CMat]//MatrixForm

(DMat = {A[[2]],A[[3]]})//MatrixForm

RowReduce[DMat]//MatrixForm

{{3,4,-1,9},{4,-2,6,-10}}//MatrixForm

RowReduce[{{3,4,-1,9},{4,-2,6,-10}}]//MatrixForm

RowReduce[{{3,4,-1},{4,-2,6}}]//MatrixForm

RowReduce[{{3,4,9},{4,-2,-10}}]//MatrixForm