input: from typing import List
  
  def add_matrix(matrix1: List[List[int]], matrix2: List[List[int]]) -> List[List[int]]:
      """ Adds two matrices. If the matrices are not compatible for addition (i.e., different number of rows or columns),
      it returns 'Matrices not compatible'. If they are compatible, it returns a new matrix which is the sum of the two input matrices.
      
      >>> add_matrix([[1, 2], [3, 4]], [[2, 3], [4, 5]])
      [[3, 5], [7, 9]]
      >>> add_matrix([[1, 2], [3, 4]], [[5, 6]])
      'Matrices not compatible'
      """
      if len(matrix1) != len(matrix2) or len(matrix1[0]) != len(matrix2[0]):
          return 'Matrices not compatible'
      
      rows = len(matrix1)
      cols = len(matrix1[0])
      result = [[matrix1[r][c] + matrix2[r][c] for c in range(cols)] for r in range(rows)]
      
      return result
output:     rows = len(matrix1)
      cols = len(matrix1[0])
      result = [[matrix1[r][c] + matrix2[r][c] for c in range(cols)] for r in range(rows)]
      
      return result