ABSTRACT
In this chapter we study a function called the determinant with many interesting properties. The most important property of the determinant is that a square matrix A E FnXn is invertible if and only if its determinant det(A) is not zero. Determinants are hard to compute directly from the definition, and for most purposes it is not necessary to compute them. However, there are clever ways for computing determinants: one of these computes the determinant of a matrix at the same time that it transforms the matrix to row echelon form via Gauss-Jordan elimination.
