If $\mathrm{\Delta }=\mid \begin{array}{ccc}{\mathrm{a}}_{11}& {\mathrm{a}}_{12}& {\mathrm{a}}_{13}\\ {\mathrm{a}}_{21}& {\mathrm{a}}_{22}& {\mathrm{a}}_{23}\\ {\mathrm{a}}_{31}& {\mathrm{a}}_{32}& {\mathrm{a}}_{33}\end{array}\mid$ and C_ij = (– 1)^i+j (determinant obtained by deleting ith row and jth column), then $\mid \begin{array}{ccc}{\mathrm{c}}_{11}& {\mathrm{c}}_{12}& {\mathrm{c}}_{13}\\ {\mathrm{c}}_{21}& {\mathrm{c}}_{22}& {\mathrm{c}}_{23}\\ {\mathrm{c}}_{31}& {\mathrm{c}}_{32}& {\mathrm{c}}_{33}\end{array}\mid ={\mathrm{\Delta }}^2$. If $\mid \begin{array}{ccc}1& \mathrm{x}& {\mathrm{x}}^2\\ \mathrm{x}& {\mathrm{x}}^2& 1\\ {\mathrm{x}}^2& 1& \mathrm{x}\end{array}\mid =7$ and $\mathrm{\Delta }=\mid \begin{array}{ccc}{\mathrm{x}}^3-1& 0& \mathrm{x}-{\mathrm{x}}^4\\ 0& \mathrm{x}-{\mathrm{x}}^4& {\mathrm{x}}^3-1\\ \mathrm{x}-{\mathrm{x}}^4& {\mathrm{x}}^3-1& 0\end{array}\mid$, then