Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE RELATIONSHIP BETWEEN THE POWERS OF AN INVERTIBLE MATRIX AND THOSE OF ITS INVERSE

  • Moucouf, Mohammed (Department of Mathematics Science Faculty Chouaib Doukkali University)
  • Published : 2012.11.15
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Abstract

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

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References

  1. F. Yilmaz and D. Bozkurt, On Adjacency matrix of one type of graph and Pell numbers, Proceedings of the World Congress on Engineering 2011 Vol I WCE 2011, July 6 - 8, 2011, London, U.K.
  2. D. Kim, S. Ryoo, T. Kim, and H. Sunwoo, An Explicit Form of a $2{\times}2$ Matrix Using a Recursive Sequence Journal of the Chungcheong Mathematical Society, 25 (2012), no. 1, 19-25. https://doi.org/10.14403/jcms.2012.25.1.019