If \( \Delta=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_...
0If \( \Delta=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right| \)
and \( c_{i j}=(-1)^{i+j} \) (determinant obtained by ith row and \( j \) th column), then
\[
\left|\begin{array}{lll}
c_{11} & c_{12} & c_{13} \\
c_{21} & c_{22} & c_{23} \\
c_{31} & c_{32} & c_{33}
\end{array}\right|=\Delta^{2} .
\]
If \( A, B, C \) are \( A=b c-a^{2}, B=c a-b^{2} \) and \( C=a b-c^{2} \)
\( 3 A B C-A^{3}-B^{3}-C^{3}=\pi^{2} \) and
\[
\Delta=\left|\begin{array}{lll}
b & c & a \\
c & a & b \\
a & b & c
\end{array}\right|
\]
then \( \sin ^{3}(\Delta)+\cos ^{3}(\Delta) \) equals
(a) 1
(b) \( -1 \)
(c) 0
(d) none of these
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