Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ ia real vector $[x_1,x_2]^T$ with length $||{\vec{x}}||$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of the following statements is correct?
A. $||P{\vec{x}}||$ $\leq$ $||{\vec{x}}||$ where at least one vector satisfies $||P{\vec{x}}||$ <$||{\vec{x}}||$
B. $||P{\vec{x}}||$ = $||{\vec{x}}||$ for all vectors ${\vec{x}}$
C. $||P{\vec{x}}||$ $\geq$ $||{\vec{x}}||$ where at least one vector satisfies $||P{\vec{x}}||$ >$||{\vec{x}}||$
D. No relationship can be established between$||{\vec{x}}||$ and $||P{\vec{x}}||$
