If \( \Delta=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_...
If \( \Delta=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right| \)
and \( c_{i j}=(-1)^{i+j} \) (determinant obtained by deleting ith row and \( j \) th column), then
\( \quad\left|\begin{array}{lll}c_{11} & c_{12} & c_{13} \\ c_{21} & c_{22} & c_{23} \\ c_{31} & c_{32} & c_{33}\end{array}\right|=\Delta^{2} \).
If \( \left|\begin{array}{ccc}1 & x & x^{2} \\ x & x^{2} & 1 \\ x^{2} & 1 & x\end{array}\right|=7 \) and
\( \Delta=\left|\begin{array}{ccc}x^{3}-1 & 0 & x-x^{4} \\ 0 & x-x^{4} & x^{3}-1 \\ x-x^{4} & x^{3}-1 & 0\end{array}\right| \), th
(a) \( \Delta=7 \)
(b) \( \Delta=343 \)
(c) \( \Delta=-49 \)
(d) \( \Delta=49 \)
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