Introduction
I first heard of the concept of determinants of matrices in middle school. It was a scalar number that was produced by a given formula, 'ad - bc'. That definition expanded to include determinants of 3 by 3 matrices, merely another method of producing a scalar number from a matrix. No more was discussed about the determinant (Nor about matrices).
Now, linear algebra has unveiled the original equation of the determinants and where the cookbook recipe of calculating determinants was derived from. Usefulness of determinants was addressed by showing that the determinant of a matrix can be used to characterize a matrix as singular or nonsingular (and the associated statements) and that to calculate inverse of a that matrix.
