# Determinants

## Introduction

As we have already seen, square matrix is ​​one that has the same number of rows and columns (ie is of type n x n). Every square matrix is ​​associated with a number which we call determinant.

Among the various applications of determinants in mathematics, we have:

• solving some types of systems of linear equations;

• calculating the area of ​​a triangle situated in the Cartesian plane, when the coordinates of its vertices are known;

## 1st order determinant

Given a 1st order square matrix M = a11, its determinant is the real number to11:

det M = la11I = a11

Note: We represent the determinant of a matrix between two vertical bars, which do not have the meaning of modulus. For example:

M = 5 det M = 5 or | 5 | = 5

M = -3 det M = -3 or | -3 | = -3

## 2nd order determinant

Given the matrix , order 2, by definition the determinant associated with M, 2nd order, is given by: Therefore, the determinant of an array of order 2 is given by the difference between the product of the main diagonal elements and the product of the secondary diagonal elements. See the following example.  Next: Minor Complement