I'm supposed to prove an invertible, but I'm not sure how, as the prof didn't talk about it in class, and the book is rather vague...

The question is this:

Let u and v be column vectors in R^n, and let A= I + u(v^T). Show that if (u^T)v =/= -1, then A is invertible and

A^-1 = I - (1/(1+((u^T)v)) (u(v^T))

Sorry about the last equation being so confusing, but that's it. I'm not sure how to prove this, since I don't even know how it works. I'm terrible at this stupid inverse matrix stuff...