anonymous
  • anonymous
Is \((AB)^{-1}=A^{-1}B^{-1}\) for square matrices A and B?
Mathematics
jamiebookeater
  • jamiebookeater
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TuringTest
  • TuringTest
yes
anonymous
  • anonymous
really? I couldn't find anything that says so. Wikipedia or google...
jim_thompson5910
  • jim_thompson5910
Shouldn't it be \(\Large (AB)^{-1}=B^{-1}A^{-1}\) ???

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anonymous
  • anonymous
Yeah that's what I thought too.
anonymous
  • anonymous
I guess the matrices I tried it out on were trivial...
jim_thompson5910
  • jim_thompson5910
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
TuringTest
  • TuringTest
Oh I totally didn't even read it... sorry :/

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