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Math Help - Show that something cannot be a ring

  1. #1
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    Feb 2009
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    Ring question

    I have been asked to show that the set of n x n real matrices with determinant 1 is not a ring.

    I've been fine with this topic so far, but this question stumped me. I'm not sure how I can go about manipulating examples of n x n matrices with the only piece of information that I have being that det(M) = 1. The only thing I can think of is linking it in some way with invertible matrices.
    Last edited by FractalMath; February 24th 2009 at 11:57 PM.
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  2. #2
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    Jul 2008
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    Well, in order for it to be a ring, it would have to be an abelian group under addition right? In particular, it would have to contain the additive identity, but what is the additive identity? What is its determinant?
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