1. The problem statement, all variables and given/known data A square matrix A is called nilpotent if A^k =0 for some k>0. Prove that if A is nilpotent then I+A is invertible. 3. The attempt at a solution My guess would be to do a proof by induction (on the size of the matrix) So for the trivial cases: Let A be a 2x2 Nilpotent matrix... thus it is of the form [0 x] [0 0] [0 0] Or [x 0] Clearly when we add I to A in this case, we get get a matrix, whose det =/= 0 Im having trouble doing the more general cases, seeing as that i cannot mentally see what nilpotent matrices of a larges size look like. Is this even the best way to approach this problem? Any help is appreciated.