In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

Laplaces rule may be used to compute a version of this quantity for its namesake tensor in order to prove the Alon-Tarsi conjecture for Latin squares of even order; that proof uses Cayleys version of this operator. The Cauchy-Binet rule generalizes it to commutative rings, while Leibnizs formula uses permutations of elements to compute it. Setting to zero the result of this operation on lambda I minus A allows us to calculate As eigenvalues. Cramers rule uses ratios of these to solve systems of linear equations. For ten points, name this quantity that is a d minus c b for a 2 by 2 matrix a b c d.
Science

The London and New York premieres of this opera featured the soprano Minnie Hauck playing the titular character, who sings the aria ""L'amour est un oiseau rebelle"" in act one. The line "love awaits you" ends the aria "Votre toast, je peux vous le rendre," which is sung by Escamillo. The title character works at a cigarette factory and convinces the soldier (*) Don Jose to become a smuggler. The well-known Habanera and Toreador Song are included in, for 10 points, what Georges Bizet opera about the titular Spanish gypsy woman
Fine Arts

A distinction between whether actions or common laws best create ideal conditions lead to the "act" and "rule" positions within this philosophical school. Characteristics like "fecundity," "intensity," and "extent" should be measured before one acts according to the "hedonic calculus" posited by this movement's founder, Jeremy Bentham. FTP John Stuart Mill wrote a book titled for what philosophy, which argues that one's actions should minimize suffering and maximize happiness

Social Science