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Unexpected groups

Published online by Cambridge University Press:  01 August 2016

W. R. Brakes
W. R. Brakes*
Affiliation:
Nene College, St. George's Avenue, Northampton NN2 7AL
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Extract

The reader should first try the following exercise, which motivates the later work.

Exercise: Prove that the set of real matrices

forms a group under the usual matrix multiplication.

This exercise comes with a guarantee that it will provoke at least a doubletake when first encountered. The usual reaction is to protest that these matrices are obviously singular, or to complain that the identity is missing from the set. Of course those familiar with this example can feel suitably smug in their rapid dismissal of these criticisms, but what was your reaction the first time you saw it?

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Type
Articles
Information
The Mathematical Gazette , Volume 79 , Issue 486 , November 1995 , pp. 513 - 520
Copyright
Copyright © The Mathematical Association 1995

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References

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