1. The problem statement, all variables and given/known data Let A = (x+1 2 ) (x+5 x+1) For what value(s) of x, if any, does A-1 exist? 2. Relevant equations 3. The attempt at a solution So let me see if I get the gist of this. An n x n matrix is invertible if and only if rank (A) = n. So unless there is a value of x which would make rank A < 2, then it is invertible. Since I can see no way to reduce both x+5 and x+1 to zero using one value, then A is invertible for all real numbers?