1. Not finding help here? Sign up for a free 30min 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!

Which makes A to be nonsingular

  1. Oct 2, 2004 #1
    Ques: Show that if A is singular then adj A is also singular. Given that I = [1/ det(A)]*A*adj (A)
    I tried to prove it by assuming adj(A) is nonsingular. so, [1/det(A)]*adj(A) is nonsingular, as well as I. Which makes A to be nonsingular. I feel like I am forcing out this proof. So, do you guys have any good suggestion to this?
  2. jcsd
  3. Oct 3, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    If A is invertible, then there is a B such that AB=1, that alos implies that B is invertible....
  4. Oct 3, 2004 #3


    User Avatar
    Science Advisor
    Homework Helper

    When you write [1/det(A)]*adj(A) you are assuming that det(A) is not zero and A is non-singular.

    In all cases A*adj(A)=det(A)*I. If A is singular, then det(A)=0. In other words, A*adj(A)=0. What does this say about adj(A)?
  5. Oct 3, 2004 #4
    thanks guys, but i still have a ques.. (sure this is easy for you guys) so you are saying if A is singular and A*adj(A)=0 then it implies that adj(A) is also singular? how can that be?
  6. Oct 3, 2004 #5


    User Avatar
    Science Advisor
    Homework Helper

    Suppose BC=0, where B and C are both square and non-zero.

    If C is non-singular, then multiply by C^(-1) to get:



    B=0, contradicting assumption of B non-zero

    If B is nonsingular multiply by B^(-1) on the left and get C=0.

    Therefore both B and C must be singular.
  7. May 10, 2005 #6

    Maybe a late reply, but since I was also looking for a proof to this (got stuck at the BC = 0 thing), just wanted to say thanks! :rofl:

    Btw, for those interested: the opposite is also true (Adj A is singular => A is singular) and much easier to prove obviously.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Which makes A to be nonsingular
  1. Which are true? (Replies: 2)