3 and 4 .Determinants and Matrices question bank (Mathematics)

For a $3 \times 3$ matrix $A$,if $A(\operatorname{adj} A) = \begin{bmatrix} -10 & 0 & 0 \\ 0 & -10 & 2 \\ 0 & 0 & -10 \end{bmatrix}$,then the value of the determinant of $A$ is:

If the elements of matrix $A$ are the reciprocals of elements of matrix $\left[\begin{array}{ccc}1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2} & 1 & \omega\end{array}\right]$,where $\omega$ is a complex cube root of unity,then: