September 20th, 2012, 07:49 AM  #1 
Member Joined: Aug 2012 Posts: 30 Thanks: 0  invertible matrix
I have some difficulty proving the bolded part of the exercise: If A is an nxn matrix establish the identity Isub(n)A^(k+1)=(Isub(n)A)(Isub(n)+A+A^2+...+A^k). Deduce that if some power of A is the zero matrix then Isub(n)A is invertible. Suppose now that A=2 2 1 1 1 0 0 0 1 1 1 0 0 1 1 1 Compute the powers (Isub(n)A)^i for i=1,2,3,4 and, by considering A=Isub(4)(Isub(4)A), prove that A is invertible and determine A1. I would be grateful for any help you are able to provide... 
September 21st, 2012, 09:47 AM  #2  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: invertible matrix Quote:
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