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

Check the true statements below:

A. Not every orthogonal set in ${\mathbb R}^n$ is a linearly independent set.
B. If the columns of an $m\times n$ matrix $A$ are orthonormal, then the linear mapping $x\rightarrow Ax$ preserves lengths.
C. An orthogonal matrix is invertible.
D. The orthogonal projection of $y$ onto $v$ is the same as the orthogonal projection of $y$ onto $cv$ whenever $c\neq 0$.
E. If a set $S= \{ u_{1},...,u_{p} \}$ has the property that $u_{i}\cdot u_{j}=0$ whenever $i\neq j$, then $S$ is an orthonormal set.