Pleeeeaaseeee proofs in linear algebra

  • Thread starter cleopatra
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  • #1
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Homework Statement



1) (AB)^-1=A^-1B^-1 A and B are nonsingular nxn
2) If A is nonsingular then A^-1 is nonsingular also and then (A^-1)^-1=A



The Attempt at a Solution



1) I do know that I have to multiply but I don´t know why. Can you tell me why??
This is how I do it:
((AB)^-1)*(A^-1B^-1 ))A(BB^-1)A^-1=A*In*A^-1=A*A^-1=In

2) ((A^-1)^-1)*A = ?????
 

Answers and Replies

  • #2
tiny-tim
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Hi cleopatra! :smile:

(try using the X2 tag just above the Reply box :wink:)
1) (AB)^-1=A^-1B^-1 A and B are nonsingular nxn

:rolleyes: Your question is wrong … it should be prove (AB)-1 = B-1A-1
 
  • #3
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ohh I see that now. Thanks :)
 
  • #4
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can you maby help me? :biggrin:
 
  • #5
tiny-tim
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well, to prove (AB)-1 = B-1A-1

what is the definition of (AB)-1 ? :wink:
 
  • #6
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the definition of (AB)-1 is
that AB is the inverce of AB

?
 
  • #7
tiny-tim
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the definition of (AB)-1 is
that AB is the inverce of AB

?

Yes :rolleyes:, but what does that mean?
 
  • #8
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it means that when I multiply it with AB I get In
Right?
 
  • #9
tiny-tim
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it means that when I multiply it with AB I get In
Right?

Right! :smile:

And that's the way you answer any question …

ask yourself what the definition is, and then prove that the definition fits …

in this case, prove that when you multiply the answer by AB, you get In :wink:
 

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