Which statement is false ?(Linear algebra problem) Let $P=\dfrac{xx^{T}}{x^{T}x}$ be an a square matrix of order n  where $x$ is a non zero column vector. Then which one of the following statement is False. 
$(A)$ P is idempotent 
$(B)$ P is orthogonal 
$(C)$ P is symmetric 
$(D)$ Rank of P is one 
In this question i only know that rank of $xx^{T}$ is $1$. And some short notes i have in my mind  are :
Eigen values of idempotent matrix are $0$ and $1$.
Eigen values of orthogonal matrix are $-1$ and $1$.
Eigen values of symmetric matrix are Real. But that is not sufficient for this problem i guess. I don't know how to deal rational functions in linear algebra. Please give me some knowledge i just started learning algebra. 

A matrix of rank $1 $ cannot be orthogonal.  Orthogonal matrices have maximal rank.
