This problem is so simple that I'm not exactly sure what they want you to do: Let A and B be n x n matrices such that AB = BA. Show that (A + B)^2 = A^2 + 2AB + B^2. Conclude that (I + A)^2 = I + 2A + A^2. We don't need to list properties or anything, just manipulate. This all seems self-evident from the distributive property, and showing that I^2 = I.