The infintesimal change in area is given by this operation applied to the Jacobean, and this quantity is equal to the product of the eigenvalues of a linear transformation.  
This quantity represents the volume of an n-dimensional parallelpiped given n vectors, while a similarly named quantity can be found by evaluating the Alexander polynomial at minus one.  The infintesimal change in area is given by this operation applied to the Jacobean, and this quantity is equal to the product of the eigenvalues of a linear transformation.  This value can be calculated by the levi-cevita permutation symbol or Laplace expansion. (*) Cramer's rule uses this operation to solve systems of linear equations, which is singular if it is equal to zero.  For 10 points, name this scalar operation on a square matrix, which for two by two matrices is given by A D minus B C.
This quantity represents the volume of an n-dimensional parallelpiped given n vectors, while a similarly named quantity can be found by evaluating the Alexander polynomial at minus one.  
{Det}erminant