Image Transformation Without Loop

The Given function works but is a bit slow due to the use of loops. Please suggest a solution without loop so that its working time can be improved

function I2 = f_transform(A, I1)
%A is an affine transformation matrix
%I1 is original image to be transformed

      s=size(A);
      if(s(1)~=3 || s(2)~=3)
          disp("Invalid Transforming Matrix");
          I2=0;
          return;
      end

      if(det(A)==0)
          disp("The given Transforming Matrix is Singular");
          I2=0;
          return;
      end

      [r, c]=size(I1);

      extremeValues = [1 1 r r ; 1 c 1 c; 1 1 1 1];

      newExtremeValues = A * extremeValues;
      minRow = floor( min( newExtremeValues(1,:) ) );
      maxRow = ceil( max( newExtremeValues(1,:) ) );
      minCol = floor( min( newExtremeValues(2,:) ) );
      maxCol = ceil( max( newExtremeValues(2,:) ) );

      I2 = zeros(maxRow - minRow + 1, maxCol - minCol + 1);

      for i = minRow:maxRow
          for j=minCol:maxCol
              b = A \ [i j 1]';
              p = b(1) / b(3);
              q = b(2) / b(3);

              if(p >= 1 && p <= r && q >= 1 && q <= c)
                  I2(i - minRow + 1, j - minCol + 1) = I1(round(p),round(q));
              end
          end
      end
      I2 = uint8(I2);
      return;

end