input: Write a function to add two matrices. The function should take two matrices as input and return the result of their addition. If the matrices are not of the same dimensions, return 'Matrices not compatible'.
  
  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
  
  assert add_matrix([[1, 2], [3, 4]], [[5, 6], [7, 8]]) == [[6, 8], [10, 12]]
  assert add_matrix([[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]) == [[8, 10, 12], [14, 16, 18]]
  assert add_matrix([[1, 2], [3, 4]], [[1, 2, 3], [4, 5, 6]]) == 'Matrices not compatible'
  assert add_matrix([], []) == []
output: def add_matrix(matrix1, matrix2):
      if len(matrix1) != len(matrix2) or len(matrix1[0]) != len(matrix2[0]):
          return 'Matrices not compatible'
      
      result = [[matrix1[i][j] + matrix2[i][j] for j in range(len(matrix1[0]))] for i in range(len(matrix1))]
      
      return result