input: 
  def add_matrix(matrix1, matrix2):
      """ Add two matrices together. If both matrices are compatible (i.e., they have the same dimensions) then
      return a new matrix that is the element-wise sum of the two input matrices. If they are not compatible,
      return the string 'Matrices not compatible'.
  
      >>> add_matrix([[1,2], [3,4]], [[5,6], [7,8]])
      [[6, 8], [10, 12]]
      >>> add_matrix([[1,2], [3,4]], [[5,6]])
      'Matrices not compatible'
      """
      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
  
output:     for i in range(rows):
          for j in range(cols):
              result[i][j] = matrix1[i][j] + matrix2[i][j]