What is the meaning of "Placetne, magistra?" and "Placet" in Gaudy Night?

Gaudy Night was written by mystery writer Dorothy L. Sayers and published in 1935. It is her tenth novel to feature her detective character Lord Peter Wimsey.
The novel ends with the Latin phrases: "Placetne, magistra?" and "Placet." The translation of these two phrases are "Does it please thee, Mistress?" and "It pleases," respectively.
In a little more detail, "Placetne, magistrata?" is asked by Lord Peter Wimsey to Harriet Vane. Harriet Vane replies with "Placet." By adding the "ne" to the end of Placet in the question means that Lord Peter Wimsey knows that he will receive a positive response. "Magistra" means mistress in the scholarly sense: Master or Mistress of the Arts. Lord Peter Wimsey is addressing Harriet Vane with her title.