In the Day 101 Casey introduced a lot of math and tried to explain everything in details.
He talked about calculating the inverse of a matrix by solving the linear system but that would involve a lot of math and it would be easy to make mistakes.
Then he introduced Gaussian elimination and explained the idea behind that.
But the thing he tried to explain is "why if you apply the elimination steps on an identity matrix you will get the inverse?".
At 55:50: He talked about the idea.
At 1:03:25 and 1:17:30 He tried to explain that but without success.
At 1:23:30 He explained why it make sense.
Actually Casey did very good job explaining and it would take me days if I want to search for this information on my own, Math is hard to understand and it is even harder if you tried to explain it.
But the explanation at the end was not satisfying even to him and there got to be a proof why that is true.
So while I was studying Linear Algebra, I found the explanation to that.
I did some search on the forums to see if someone did explain that, but I didn't find anything and I thought it would be nice to share that
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Sorry but I don't know other way to insert equations.