anonymous
  • anonymous
Suppose A, B and X are invertible matrices such that BinverseXA = AB: Find an expression for X in terms of A and B.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[BX^{-1}A=AB\]
anonymous
  • anonymous
I have a question to see if I'm doing this right. Do I first times each side by the inverse of B to get rid of it then by X??
anonymous
  • anonymous
What does it mean that it is invertible

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anonymous
  • anonymous
determinant is not equal to zero
anonymous
  • anonymous
Does that mean I can move them around any special way? I'm so confused
anonymous
  • anonymous
say wuttt
anonymous
  • anonymous
I still don't know how to do this :(
anonymous
  • anonymous
is that from linear algebra class in college?
anonymous
  • anonymous
yes
anonymous
  • anonymous
If the matrix A is invertible, that means there exists a matrix\[A^{-1}\]such that:\[AA^{-1}=A^{-1}A=I\]where I is the identity matrix.
anonymous
  • anonymous
Okay I know that but I still want to know if what I wrote up there is on the right track
TuringTest
  • TuringTest
yes, multiply both sides by \(B^{-1}\) and what do you get?
anonymous
  • anonymous
you get \[x^{-1} A = B^{-1}AB\] so I went on and multiplied each side by X and then got \[A=XB^{-1}AB\] But I'm confused beacuse it doesn't look right
TuringTest
  • TuringTest
I'm having a little trouble too actually :/ while I work on it, I can say that you can use \(AB=B^{-1}AB\) to make that a little prettier, but I still can't solve for \(X\) yet
anonymous
  • anonymous
sorry my laptop decided to restart lol. So you're not allowed to rearrange the letters at all, right?
anonymous
  • anonymous
or where did you get the B to? on the right side
TuringTest
  • TuringTest
no, matrix multiplication is not commutative (cant move the letters)
TuringTest
  • TuringTest
oh I see, I misread the question, sorry
TuringTest
  • TuringTest
\[BX^{-1}A=AB\] all matrices are invertible solve for \(X\) correct?
anonymous
  • anonymous
Yup!
anonymous
  • anonymous
I tried switching them around in different ways but nothing works lol
TuringTest
  • TuringTest
yeah, there must be some trick we're missing :/
anonymous
  • anonymous
Like there's no way to rearrange it so that BA=AB ?
TuringTest
  • TuringTest
only if BA and AB are inverses of each other, which I am trying to prove... so far unsuccessfully.
TuringTest
  • TuringTest
I mean if A and B are inverses of each other, then AB=BA=I
anonymous
  • anonymous
I think I'll just leave it and wait for the solution to be posted online to understand it lol thanks a lot for your help though!
TuringTest
  • TuringTest
This will continue to bother me, please let me know the answer when you find out :) Sorry I couldn't really help.
anonymous
  • anonymous
I really appreciate that you tried! I'll post the answer when it's up!

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