Let $A = \begin{pmatrix} 0 & -2 \\ 2 & 0 \end{pmatrix}$. If $M$ and $N$ are two matrices given by $M = \sum _ { k = 1 } ^ { 10 } A ^ { 2k }$ and $N = \sum _ { k = 1 } ^ { 10 } A ^ { 2k - 1 }$ then $MN^{2}$ is\\
(1) a non-identity symmetric matrix\\
(2) a skew-symmetric matrix\\
(3) neither symmetric nor skew-symmetric matrix\\
(4) an identity matrix