THE RELATIONSHIP BETWEEN THE POWERS OF AN INVERTIBLE MATRIX AND THOSE OF ITS INVERSE

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 $A^{-n}\;=\;(A_{i,j}{(-n))$ .