Help me /sci/, I know I'm fucking this simple problem up.

>>9069849
Whoops, forgot to change the sign for when I added I to both sides. But the point still stands.

>>9069849
>but should I have written there doesn't exist an X?
yes, A-I =A is the contradiction you got by assuming it does exist

>>9069849
>>9069855

God, I say this but then looking at the equation it's pretty obvious that the trivial solution exists at least, where A ultimately equals -I and X is the zero matrix.

What the fuck is wrong with my math.

>>9069849
>X = I - inverse A which means
>A(I - inverse A) = A
...

>>9069857
But what about where X is the zero matrix and A is -In?

>>9069860
Oh shit, I'm an idiot, thank you!

It's A(I+inverse A)-I = A, so I get A+I-I=A

Which makes fucking sense.

Thank god.

>>9069849

[math] AX-I=A, AX=A+I, X=I+A^{-1} [/math]

???

>>9069887
Yeah, I fucked the sign up when I was writing out my answer, and apparently when I plugged it back in to make sure it worked I completely ignored the fact you were subtracting I from AX for some reason.

So assuming that I didn't fuck up the sign like a retard and that I left my answer at X=inverseA(A+I) I think I should get full credit.

>>9069849
If such a matrix X existed then we'd have
AX-I_n=A
AX-A=I_n
A(X-I_n)=I_n

so A would be invertible.

>>9070090
deserves recognition. nice