Urgent help needed on the following question on matrices in linear algebra:
Let A be an nxn square matrix such that A^2=0. Show that I+A is invertible and that (I+A)^-1=I-A.
(Where I is the identity matrix).
thanks
To show that I+A is invertible you need to show that there is an inverse matrix. There is! The inverse matrix is I-A because (I+A)(I-A) = I^2 - A^2 = I^2 = I.