Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

vf321

  • 3 years ago

Is \((AB)^{-1}=A^{-1}B^{-1}\) for square matrices A and B?

  • This Question is Closed
  1. TuringTest
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  2. vf321
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    really? I couldn't find anything that says so. Wikipedia or google...

  3. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Shouldn't it be \(\Large (AB)^{-1}=B^{-1}A^{-1}\) ???

  4. vf321
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah that's what I thought too.

  5. vf321
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I guess the matrices I tried it out on were trivial...

  6. jim_thompson5910
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    AB = C (AB)^(-1)(AB) = (AB)^(-1)C I = (AB)^(-1)AB I = B^(-1)A^(-1)AB I = B^(-1)[A^(-1)A]B I = B^(-1)[I]B I = B^(-1)B I = I It's explained better here http://mathworld.wolfram.com/MatrixInverse.html

  7. TuringTest
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh I totally didn't even read it... sorry :/

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy