input: from typing import List, Union
  
  
  def add_matrix(matrix1: List[List[int]], matrix2: List[List[int]]) -> Union[str, List[List[int]]]:
      """
      Adds two matrices. If the matrices are not compatible for addition (i.e., they do not have the same dimensions), returns 'Matrices not compatible'. Otherwise, returns the resulting matrix from the addition.
      
      >>> add_matrix([[1, 2], [3, 4]], [[5, 6], [7, 8]])
      [[6, 8], [10, 12]]
      >>> add_matrix([[1, 2], [3, 4]], [[10], [20]])
      'Matrices not compatible'
      """
output:     if len(matrix1) != len(matrix2) or any(len(row1) != len(row2) for row1, row2 in zip(matrix1, matrix2)):
          return 'Matrices not compatible'
      
      result = []
      for row1, row2 in zip(matrix1, matrix2):
          result.append([a + b for a, b in zip(row1, row2)])
      
      return result