input: from typing import List
  
  def add_matrix(matrix1: List[List[int]], matrix2: List[List[int]]) -> List[List[int]] or str:
      """ Add two matrices if they are compatible.
      >>> add_matrix([[1, 2], [3, 4]], [[5, 6], [7, 8]])
      [[6, 8], [10, 12]]
      >>> add_matrix([[1, 2], [3, 4]], [[5, 6]])
      'Matrices not compatible'
      """
      if len(matrix1) != len(matrix2):
          return 'Matrices not compatible'
      if len(matrix1[0]) != len(matrix2[0]):
          return 'Matrices not compatible'
      
      rows = len(matrix1)
      cols = len(matrix1[0])
      result = [[matrix1[i][j] + matrix2[i][j] for j in range(cols)] for i in range(rows)]
      
      return result
output:     rows = len(matrix1)
      cols = len(matrix1[0])
      result = [[matrix1[i][j] + matrix2[i][j] for j in range(cols)] for i in range(rows)]
      
      return result