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If \( \mathrm{A} \) is a symmetric and \( \mathrm{B} \) skew symmetric matrix and \( \mathrm{A}+\mathrm{B} \) is non singular and \( \mathrm{C}=(\mathrm{A}+\mathrm{B})^{-1}(\mathrm{~A}-\mathrm{B}) \) then \( \mathrm{C}^{\mathrm{T}} \mathrm{AC} \)
(A) \( \mathrm{A}+\mathrm{B} \)
(B) \( \mathrm{A}-\mathrm{B} \)
(C) \( \mathrm{A} \)
(D) \( B \)
\( \mathrm{P} \)
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