Recently I have previewed something about linear algebra. And I found an interesting problem. It can be viewed as a small general conclusion. $A$ is an invertible matrix, $\alpha$ and $\beta$ are two n-dimensional column vectors. Then $$1 + {\beta ^T}{A^{ - 1}}\alpha \ne 0$$ How to Calculate the inverse matrix of $$A + \alpha {\beta ^T}$$
Any ideas? Thanks in advance.