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vf321

  • 2 years ago

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

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  1. TuringTest
    • 2 years ago
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    yes

  2. vf321
    • 2 years ago
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    really? I couldn't find anything that says so. Wikipedia or google...

  3. jim_thompson5910
    • 2 years ago
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    Shouldn't it be \(\Large (AB)^{-1}=B^{-1}A^{-1}\) ???

  4. vf321
    • 2 years ago
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    Yeah that's what I thought too.

  5. vf321
    • 2 years ago
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    I guess the matrices I tried it out on were trivial...

  6. jim_thompson5910
    • 2 years ago
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    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
    • 2 years ago
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    Oh I totally didn't even read it... sorry :/

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