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!

Inverse of Matrix Problem

  1. Jun 16, 2014 #1
    Show that if A, B and A+B are invertible matrices with the same size, then

    What does the result in the first part tell you about the matrix $$(A^{-1}+B^{-1})$$?

    I get the first part. Help me with the second part. My book says that the matrix $$(A^{-1}+B^{-1})$$ is not equal to $$(A+B)^{-1}$$
    How did they mathematically prove that?
  2. jcsd
  3. Jun 16, 2014 #2


    User Avatar
    Homework Helper
    Gold Member

    Multiply ##(A^{-1}+B^{-1})## with ##(A+B)##. Do you get ##I##?

  4. Jun 16, 2014 #3


    User Avatar
    Homework Helper

    Think about it, is adding two matrices together and then taking the inverse of the resulting matrix the same as taking the inverse of the two matrices individually and summing the result? If you try this for some easy 2x2 cases you will see it does not hold.
  5. Jun 17, 2014 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    Does it surprise you? For a and b numbers, [itex]\frac{1}{a}+ \frac{1}{b}[/itex] is generally NOT equal to [itex]\frac{1}{a+ b}[/itex].
  6. Jun 17, 2014 #5


    User Avatar
    Science Advisor
    Homework Helper

    Hmmm .... the statement that ##(A^{-1} + B^{-1}) \ne (A+B)^{-1}## should be rather "obvious" for the reasons given in the other posts, but I don't quite see the why the result of the first part should make you think of it.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Inverse of Matrix Problem
  1. Matrix-inverse problem (Replies: 2)

  2. Inverse Matrix Problem (Replies: 6)

  3. Inverse matrix problem (Replies: 13)