If  $w$  is an imaginary cube root of unity, find the value of $\left|\begin{array}{ccc}1& w& w^2\\ w& w^2& 1\\ w^2& 1& w\end{array}\right|$

Let $A=\left[a_{ij}\right]$ be a square matrix of order $3\times 3$ and $C_{ij}$ denote cofactor of $a_{ij}$ in $A$. If $\left|A\right|=5$, write the value of $a_{31}{C}_{31}+a_{32}{C}_{32}+a_{33}{C}_{33}$

Let $A=\left[a_{ij}\right]$ be a square matrix of order $3\times 3$ and $C_{ij}$ denote cofactor of $a_{ij}$ in $A$. If $\left|A\right|=5$, write the value of 

 $a_{11}{\mathrm{C}}_{21}+a_{12}{\mathrm{C}}_{22}+a_{13}{\mathrm{C}}_{23}$.