input: The function described will calculate the sum of two matrices with the provided function signature. Below is the implementation of the function `add_matrix`, followed by test cases and their expected output.
  
  
  def add_matrix(matrix1, matrix2):
      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
  
  # Test cases:
  >>> add_matrix([[1, 2], [3, 4]], [[2, 3], [4, 5]])
  [[3, 5], [7, 9]]
  >>> add_matrix([[1, 2], [3, 4]], [[5, 6, 7], [8, 9, 10]])
  'Matrices not compatible'
  
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
  