1) Is there a way we can prove that there always exists an inverse matrix (well actually one doesn't always exist) but that the determinant must not be 0 in order to find it? I also don't understand how the 3.9 proof is proving it.
2) I am so used to just using the fact that the numbers I work with are part of a ring so I can perform all of these operations, but I haven't thought about how we need to prove all of these theorems in the first place, before we can even consider using them for practical use.
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