Examples of Gauss-Jordan elimination

Sample answer
    To obtain the inverse matrix, we define a matrix in which the matrix $A$ and the identity matrix $I$ are arranged side by side, . This matrix is called augmented matrix. We transform the matrix $A$ in the augumented matrix to the identity matrix $I$ by performing elementary row operations, i.e., . As a result, the identity matrix in the right half of the augmented matrix becomes the inverse of $A$. This method of finding the inverse matrix is called Gauss-Jordan elimination. (Here, the dotted line drawn vertically is merely a convenience for distinguishing between the left side and the right side.)
  According to this method, we perform elementary row operations as follows.   Therefore, we obtain

Sample answer
    To obtain the inverse matrix, we define a matrix in which the matrix $A$ and the identity matrix $I$ are arranged side by side, . This matrix is called augmented matrix. We transform the matrix $A$ in the augumented matrix to the identity matrix $I$ by performing elementary row operations, i.e., . As a result, the identity matrix in the right half of the augmented matrix becomes the inverse of $A$. This method of finding the inverse matrix is called Gauss-Jordan elimination. (Here, the dotted line drawn vertically is merely a convenience for distinguishing between the left side and the right side.)
  According to this method, we perform elementary row operations as follows.   Therefore, we obtain