A doubt regarding the calculation of inverse matrices

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I am attaching the solution of a school question asking to calculate the inverse of a matrix. However, the solution proposed does not fit in anything I ever seen about calculating inverse matrices. I did not found any property that fits the final part of the solution (the one I highlighted in the image below) although the solution is correct, I would like to know which property or reasoning supports the final solution of such a problem. Thanks. enter image description here