Let $D_{k} = \begin{vmatrix} 1 & 2k & 2k-1 \\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix}$. If $\sum_{k=1}^{n} D_{k} = 96$,then $n$ is equal to

If $A=\begin{bmatrix} 1 & 1 & 0 \\ 2 & 1 & 5 \\ 1 & 2 & 1 \end{bmatrix}$,then $a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23} = \dots$

The value of the determinant $\left| \begin{matrix} 0 & x - y & x - z \\ y - x & 0 & y - z \\ z - x & z - y & 0 \end{matrix} \right|$ is:

By using properties of determinants,show that:
$\left|\begin{array}{ccc}0 & a & -b \\ -a & 0 & -c \\ b & c & 0\end{array}\right|=0$

The value of $\left| \begin{matrix} \sin \alpha & \cos \alpha & \sin(\alpha + \gamma) \\ \sin \beta & \cos \beta & \sin(\beta + \gamma) \\ \sin \delta & \cos \delta & \sin(\delta + \gamma) \end{matrix} \right|$ is

$\left| {\begin{array}{*{20}{c}} 1 & 5 & \pi \\ {{\log }_e}e & 5 & {\sqrt 5 } \\ {{\log }_{10}}10 & 5 & e \end{array}} \right| = $