Question

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

Answer 1

yes

Answer 2

really? I couldn't find anything that says so. Wikipedia or google...

Answer 3

Shouldn't it be

\(\Large (AB)^{-1}=B^{-1}A^{-1}\)

???

Answer 4

Yeah that's what I thought too.

Answer 5

I guess the matrices I tried it out on were trivial...

Answer 6

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

Answer 7

Oh I totally didn't even read it... sorry :/