input: Write a function to add two matrices. The function should first check if the matrices are of the same dimensions. If they are not, return 'Matrices not compatible'. If they are, add the corresponding elements of both matrices and return the resultant matrix.
  
  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 = [[matrix1[i][j] + matrix2[i][j] for j in range(cols)] for i in range(rows)]
      
      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],[4,5,6]], [[1,2],[3,4]])=='Matrices not compatible'
  assert add_matrix([[1,2]], [[3,4]])==[[4, 6]]
  assert add_matrix([], [])=='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