JEE Math Practice Question

Let $$A = \left[ {\begin{matrix} 0 & { - 2} \\ 2 & 0 \\ \end{matrix} } \right]$$. If M and N are two matrices given by $$M = \sum\limits_{k = 1}^{10} {{A^{2k}}} $$ and $$N = \sum\limits_{k = 1}^{10} {{A^{2k - 1}}} $$ then MN2 is :

1. A.a non-identity symmetric matrix
2. B.a skew-symmetric matrix
3. C.neither symmetric nor skew-symmetric matrix
4. D.an identity matrix