Prove det(I + uv^T) = 1 + v^T u for u,v in R^n

[Amer]

\[ \text{Let u,v } \in \mathbb{R}^n \;\; \text{Show that } \;\;, Det(I + uv^T) = 1 + v^T u \]

I is the identity matrix nxn
any hints ?

 

[Evgeny.Makarov]

This is a special case of the Matrix determinant lemma.