Determinant calculation of a square matrix is widely used in solving many applied Mathematics problems. Some of them are while solving a set of linear equations using Cramer's rule (iff they have unique solutions), calculation of inverse matrix, Eigen values/ Eigen vectors problem and so on.

The determinant of a square matrix A∈R

det(A) = SUM

.

The determinant of a square matrix A∈R

^{n×n}is the real number det(A) defined as follows:det(A) = SUM

_{perm }[sign(ν1,ν2,...,νn)a1ν1a2ν2...anνn].