The determinants of the reverse identity matrices are defined as follow: \( \left|J_{1}\right|=|1|=+1,\left|J_{2}\right|=\left|\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right|=-1,\left|J_{3}\right|= \) \( \left|\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right|=-1, \cdots \) Find the determinant of \( \mathrm{J}_{100} \) .

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