1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Inverses of matrices

  1. Aug 25, 2008 #1
    1. The problem statement, all variables and given/known data
    hi, i have 2 nxn matrices A and B i found that (AB)^-1=A^-1xB^-1 but how do i do

    plz i really need some help here im kinda lost i have

    anyone have any ideas?
  2. jcsd
  3. Aug 25, 2008 #2


    User Avatar
    Science Advisor

    Well, it's really unfortunate that you "found" that because it is not true!

    No! you can't cancel BA-1! That's why (AB)-1 is NOT A-1B-1.

    In order to be able to "cancel" A with A-1 or B with B-1, because multiplication of matrices is not commutative, you have to reverse the order of multiplication. (AB)(B-1A-1)= A(BB-1)A-1= A(I)A-1= AA-1= I. (AB)-1= B-1A-1.

    One thing you could do is think of (A2B2)-1 as (UV)-1= V-1U-1 where U= A2 and V= B2- that is (A2B2)-1= (B2)-1(A-1)2= (A-1)2(B-1)2.

    Similarly, (AABB)(B-1B-1A-1A-1)= AAB(BB-1)B-1A-1A-1= AA(B-1B-1)A-1A-1= A(AA-1)A-1= AA-1= I

    Last edited by a moderator: Aug 25, 2008
  4. Aug 25, 2008 #3
    oh yes... sorry that was a typo it should of been B^-1A^-1 because of socks and shoes formula..... sorry, ok yes i understand what u mean, yer i kept thinking of it as A^2 and B^2 instead of AA and BB just got myself confused... thankyou heaps!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook