input: from typing import List
  
  def add_matrix(matrix1: List[List[float]], matrix2: List[List[float]]) -> List[List[float]] or str:
      """
      This function adds two matrices. If the matrices are not compatible (i.e., they do not have the same dimensions),
      it returns the string 'Matrices not compatible'. Otherwise, it returns the sum of the two matrices.
      
      >>> 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 = [[sum(row) for row in zip(*size)] for size in zip(matrix1, matrix2)]
      
      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