All vectors are in ${\mathbb R}^n$.

Check the true statements below:

A. $u\cdot v-v\cdot u=0$.
B. For an $m\times n$ matrix $A$, vectors in the null space of $A$ are orthogonal to vectors in the row space of $A$.
C. If $||u||^{2}+||v||^{2}=||u+v||^{2}$, then $u$ and $v$ are orthogonal.
D. If $x$ is orthogonal to every vector in a subspace $W$, then $x$ is in $W^{\perp}$.
E. For any scalar $c$, $||cv||=c||v||$.