So my teacher said that when proving something, I can't start out with what I'm trying to prove. But what if it is an "if this than that proof"(adsbygoogle = window.adsbygoogle || []).push({});

For example,

If A(squared)=A, then I-A=(I-A)inverse

Well, I started using what I'm trying to prove by multiplying both sides by I-A

I get (I-A)squared=I

implies I-4A+4AA=I

implies I-4A+4A=I b/c A(squared)=A using the hypothesis

implies I+0=I

implies I=I both sides equal

The thing is that I have proven that if AA=A, then I-A=(I-A)inverse by using the hypothesis somewhere in the solution. Would this be a logical conclusion?

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# Confused about this logic

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