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: Linear Algebra: Prove that the set of invertible matrices is a Subspace

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Is U = {A| A [itex]\in[/itex] nn, A is invertible} a subspace of nn, the space of all nxn matrices?

    3. The attempt at a solution
    This is easy to prove if you assume the regular operations of vector addition and scalar multiplication. Then the Identity matrix is in the set but 0*I and I + (-I) are not, so its not closed under vector addition or scalar multiplication. Is there a way to prove this without assuming the usual vector operations?
  2. jcsd
  3. Jan 27, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Not until they tell you what the alternative addition and multiplication operations are. I don't think you have to worry about that. Your examples are just fine.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook