请将以下的英文翻译为中文：In this lesson, we will show how the inverse of a matrix can be derived using a technique known as the Gauss-Jordan (or reduced row) elimination method. Finding the inverse of a matrix implies a couple of things, starting with the fact that the matrix is invertible in the first place (a matrix is not necessarily invertible). First, to be invertible, a matrix has to be a square matrix (it has as many rows as it has columns, for instance, 2x2, 3x3, 4x4, etc.), and also the determinant of the matrix has to be different than zero (to learn about the determinant of a matrix refer to Geometry: Matrix Operations). Any matrix with a zero determinant is said to be singular (meaning it is not invertible).

Before we get started, remember that a matrix can be seen as a system of linear equations that can be solved using what we call row elementary operations. Row elementary operations have the property to preserve the solution set by the matrix. There are three such operations:

Operation 1: swapping rows of a matrix.

Operation 2: multiplying each coefficient of a row by a non-zero constant 
. Note that we say multiplying here, which implies that this can be a division too. We can multiply coefficients by 
 
, which is the same as dividing the coefficients by 2. Similarly, this constant can be positive or negative, 2 or -2.

Operation 3: replacing a row with the sum of itself and the multiple of another row. For instance, we can add the coefficients of row 4 to those of row 1. But we can also, in the process, multiply the coefficients of row 4 by some constant 
 as follows: