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Homework Help: Invertible 3x3 matrices a subspace of 3x3 matrices

  1. Jul 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Is the set of invertible 3x3 matrices a subspace of 3x3 matrices?

    2. Relevant equations



    3. The attempt at a solution
    I think no - the 'neutral 0 element' is not in the subset since the 3x3 0 matrix is not in the subset. Am I right? The book says it's not a subspace because it's not closed under addition, but I'm not sure if my reason is also correct.
     
  2. jcsd
  3. Jul 11, 2010 #2

    Dick

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    Your reason is also correct.
     
  4. Jul 11, 2010 #3
    thanks! also, quick question: does the 'neutral 0 element' mean the additive identity?
     
  5. Jul 11, 2010 #4

    Dick

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    Sure, subspace generally means closed under linear combinations. The zero matrix is the identity.
     
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