## 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 = a_{11}, its determinant is the real number to_{11}:

det M = la_{11}I = a_{11}

*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