input: Write a function to add two matrices. Ensure that the matrices are of the same size, otherwise return a message indicating incompatibility. If compatible, return the resulting matrix after addition.
  
  ### Input:
  matrix1 = [[1, 2, 3], [4, 5, 6]]
  matrix2 = [[7, 8, 9], [10, 11, 12]]
  
  ### 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
  
  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]]
  assert add_matrix([[1, 2]], [[3, 4]]) == [[4, 6]]
  assert add_matrix([[1], [2]], [[3], [4]]) == [[4], [6]]
  assert add_matrix([[1, 2], [3, 4]], [[5, 6], [7, 8]]) == [[6, 8], [10, 12]]
  assert add_matrix([[1, 2], [3, 4]], [[5], [6]]) == 'Matrices not compatible'
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