I recently jumped into linear algebra from Calculus and I'm confused by all this freedom that is given to me. I mean, I'm free to run any row operation I want at whichever order I want as long as the end result is an identity matrix. It's confusing and I can get many different results from this process. I still haven't correctly found a single inverse by myself. Every time I try row operations, the 3x3 inverse matrix ends up having 7 or 8 zeros and some irrelevant numbers.Then I try the determinant method but it still ends up being nowhere close to the right solution. What do anons?