Assume A = [(1,0,-2),(-1,3,2),(5,0,-1)]is a matrix, then find the inverse of A.
I have tried to find the inverse of A this way:
However, I don't understand what's wrong in the following solution instead.
2026-04-04 12:43:53.1775306633
Why I cannot find the inverse matrix of A with the second method?
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![Assume A = [(1,0,-2),(-1,3,2),(5,0,-1)]is a matrix, then find the inverse of A. I have tried to find the inverse of A this way:](https://i.stack.imgur.com/9L5ki.png){kind=link}
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The second approach fails when you "cancel" $A-3I$, because it's quite possible that $A-3I$ doesn't have an inverse.
One way to check this sort of thing in general is to take the answer you got at the end and substitute it in for "A" in each previous line, and see where you start to not get equality any more; that's where your mistake is.