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Patterns among square roots of the 2 × 2 identity matrix

Published online by Cambridge University Press:  15 February 2024

Howard Sporn
Howard Sporn*
Affiliation:
Department of Mathematics and Computer Science, Queensborough Community College, Bayside, NY, USA 11364 e-mail: hsporn@qcc.cuny.edu

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The 2 × 2 identity matrix, $${I_2} = \left( \begin{gathered}{\rm{1 \,\,\,0}} \hfill \\{\rm{0 \,\,\,1}} \hfill \\ \end{gathered}\right)$$, has an infinite number of square roots. The purpose of this paper is to show some interesting patterns that appear among these square roots. In the process, we will take a brief tour of some topics in number theory, including Pythagorean triples, Eisenstein triples, Fibonacci numbers, Pell numbers and Diophantine triples.

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Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 571 , March 2024, pp. 84 - 93
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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