THE RELATIONSHIP BETWEEN THE POWERS OF AN INVERTIBLE MATRIX AND THOSE OF ITS INVERSE
Mohammed Mouçouf · Journal of the Chungcheng Mathematical Society · 2012
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 $A^{-n}\;=\;(A_{i,j}{(-n))$ .