Why does $\mathbf{Var}(X) = \mathbf{Var}(-X)$ for random variable $X$? Question from UCLA Math GRE study packet, Problem Set 2, Number 4:
http://www.math.ucla.edu/~cmarshak/GREProb.pdf
Let $X$ and $Y$ be random variables. Which of the following is always true?
\begin{align}
...\\
(II) \ \mathbf{Var}(X) = \mathbf{Var}(-X)\\
...\\
...\\
\end{align}
Answer says (II) is True. Why?

Another way to realize this is to 
$$
\begin{align}
0&=\mathrm{Var}(0)=\mathrm{Var}(X+(-X))=\mathrm{Var}(X)+\mathrm{Var}(-X)-2\mathrm{Cov}(X,X)\\
&=\mathrm{Var}(X)+\mathrm{Var}(-X)-2\mathrm{Var}(X)=\mathrm{Var}(-X)-\mathrm{Var}(X).
\end{align}
$$
