# Pleeeeaaseeee proofs in linear algebra

## 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 = ?????

tiny-tim
Homework Helper
Hi cleopatra! (try using the X2 tag just above the Reply box )
1) (AB)^-1=A^-1B^-1 A and B are nonsingular nxn Your question is wrong … it should be prove (AB)-1 = B-1A-1

ohh I see that now. Thanks :)

can you maby help me? tiny-tim
Homework Helper
well, to prove (AB)-1 = B-1A-1

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

?

tiny-tim
Homework Helper
the definition of (AB)-1 is
that AB is the inverce of AB

?

Yes , but what does that mean?

it means that when I multiply it with AB I get In
Right?

tiny-tim
Homework Helper
it means that when I multiply it with AB I get In
Right?

Right! 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 