1. The problem statement, all variables and given/known data http://img144.imageshack.us/my.php?image=matrixkx2.jpg Find the sum of the infinte series: I3+A+A2+A3... 2. Relevant equations A*I=I*A=A A*A-1=A-1*A=I And probably some other things as well. 3. The attempt at a solution This is my (our) solution to this problem, could someone check and see if we actually can do all of this mathematically? Matrices are .. fairly new. (Say, three weeks or so.) S=the infinite sum S=I3+A+A2+A3... AS=IA+A2+A3... S - AS=I3+A+A2+A3... - IA+A2+A3... S - AS=I S(I - A)=I S(I - A)(I - A)-1=I(I - A)-1 SI=(I - A)-1 S=(I - A)-1 From this we just calculate I - A, which is simple enough, and then take (I-A)*X=I, X being our inverse matrix with entries something like a through i. Just doing matrix multiplication we get nine expressions for the different nine terms and in the end get a matrix, which is then the inverse matrix of (I - A). Is this a good solution for this problem?