• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Pleeeeaaseeee proofs in linear algebra

  • Thread starter cleopatra
  • Start date
1. 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



3. 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 = ?????
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
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
 
ohh I see that now. Thanks :)
 
can you maby help me? :biggrin:
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
well, to prove (AB)-1 = B-1A-1

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

?
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
it means that when I multiply it with AB I get In
Right?
 

tiny-tim

Science Advisor
Homework Helper
25,790
246
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:
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top