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!

Finding inverse from matrix equation

  1. Oct 26, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose that a square matrix ##A## satisfies ##(A - I)^2 = 0##. Find an explicit formula for ##A^{-1}## in terms of ##A##

    2. Relevant equations


    3. The attempt at a solution
    From manipulation we find that ##A^2 - 2A + I = 0## and then ##A(2I - A) = I##. This shows that if we right-multiply ##A## by ##2I - A##, we get the identity matrix. However, to show that ##2I - A## is an inverse, don't we also have to show that we can left-multiply ##A## by ##2I - A## such that ##(2I - A)A = I##? I don't see how we can do that...
     
  2. jcsd
  3. Oct 26, 2016 #2

    DrClaude

    User Avatar

    Staff: Mentor

    I don't think that showing that ##(2I - A)A = A(2I - A)## should be too difficult.
     
  4. Oct 26, 2016 #3

    fresh_42

    Staff: Mentor

    Yes.
    Multiply it.
     
  5. Oct 26, 2016 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    There is a standard theorem which states that if a square matrix ##A## has a right (left) inverse ##B##, then it also has a left (right) inverse, and that is equal to ##B## as well. You should expand your understanding by trying to prove that theorem.
     
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: Finding inverse from matrix equation
Loading...