Determinant

In linear algebra, a determinant is a function depending on n that associates a scalar det(A) to every n×n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor for volume when A is regarded as a linear transformation. Determinants are important both in calculus, where they enter the substitution rule for several variables, and in multilinear algebra.

Example

Suppose we want to compute the determinant of

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:A = egin{bmatrix}-2&2&-3\

~ ~ ~ ~ ~ ~ ~ ~ ~ ~