Originally Posted by

**deniselim17** I have no idea where to start to prove this.

Let $\displaystyle A=I_{n} -u^{T}u \in M_{n}(R)$ where $\displaystyle I_{n}$ is the identity, $\displaystyle u$ is a non-zero row vector in $\displaystyle R^{n}$ and $\displaystyle u^{T}$ denotes transpose of $\displaystyle u$. If $\displaystyle A$ is symmetric, show that $\displaystyle u^{T}u=I_{n}$.

$\displaystyle I_{n}, u^{T}u$ both symmetric, then of course $\displaystyle A$ is symmetrc. But how to show $\displaystyle u^{T}u$ is equal to identity?