Matrices And Determinants

Let $$\mathrm{D}_{\mathrm{k}}=\left|\begin{array}{ccc}1 & 2 k & 2 k-1 \\ n & n^{2}+n+2 & n^{2} \\ n & n^{2}+n & n^{2}+n+2\end{array}\right|$$. If \(\sum_\limits{k=1}^{n} \mathrm{D}_{\mathrm{k}}=96\), then \(n\) is equal to _____________.