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\[BX^{-1}A=AB\]

What does it mean that it is invertible

determinant is not equal to zero

Does that mean I can move them around any special way? I'm so confused

say wuttt

I still don't know how to do this :(

is that from linear algebra class in college?

yes

Okay I know that but I still want to know if what I wrote up there is on the right track

yes, multiply both sides by \(B^{-1}\) and what do you get?

or where did you get the B to? on the right side

no, matrix multiplication is not commutative (cant move the letters)

oh I see, I misread the question, sorry

\[BX^{-1}A=AB\] all matrices are invertible
solve for \(X\)
correct?

Yup!

I tried switching them around in different ways but nothing works lol

yeah, there must be some trick we're missing :/

Like there's no way to rearrange it so that BA=AB ?

only if BA and AB are inverses of each other, which I am trying to prove... so far unsuccessfully.

I mean if A and B are inverses of each other, then AB=BA=I

I really appreciate that you tried! I'll post the answer when it's up!