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If \( \mathrm{A} \) is a skew-symmetric matrix of order 2 and \( \mathrm{B} \),
P \( C \) are matrices \( \left[\begin{array}{ll}1 & 4 \\ 2 & 9\end{array}\right],\left[\begin{array}{cc}9 & -4 \\ -2 & 1\end{array}\right] \) respectively,

W then \( \mathrm{A}^{3}(\mathrm{BC})+\mathrm{A}^{5}\left(\mathrm{~B}^{2} \mathrm{C}^{2}\right)+\mathrm{A}^{7}\left(\mathrm{~B}^{3} \mathrm{C}^{3}\right)+\ldots+\mathrm{A}^{2 n+1} \) \( \left(\mathrm{B}^{n} \mathrm{C}^{n}\right) \), is
(A) a symmetric matrix
(B) a skew-symmetric matrix
(C) an identity matrix
(D) None of these
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