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(A) Let $\Delta = \left| \begin{array}{ccc} pa & qb & rc \ qc & ra & pb \ rb & pc & qa \end{array} ight|$.Expanding the determinant,we get:$\Delta

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(A) Let $\Delta = \left| \begin{array}{ccc} pa & qb & rc \ qc & ra & pb \ rb & pc & qa \end{array} ight|$.Expanding the determinant,we get:$\Delta = pa(ra \cdot qa - pb \cdot pc) - qb(qc \cdot qa - pb \cdot rb) + rc(qc \cdot pc - ra \cdot rb)$$= pa(qa^2r - pbc^2) - qb(q^2ac - prb^2) + rc(qpc^2 - r^2ab)$$= pqr(a^3) - p^2abc - q^3abc + pqr(b^3) + pqr(c^3) - r^3abc$$= pqr(a^3 + b^3 + c^3) - abc(p^3 + q^3 + r^3)$.Given that $p + q + r = 0$,we know that $p^3 + q^3 + r^3 = 3pqr$.Similarly,given that $a + b + c = 0$,we know that $a^3 + b^3 + c^3 = 3abc$.Substituting these values into the expression for $\Delta$:$\Delta = pqr(3abc) - abc(3pqr) = 3pqrabc - 3pqrabc = 0$.

If $p + q + r = 0$ and $a + b + c = 0$,then the value of the determinant $\left| \begin{array}{ccc} pa & qb & rc \\ qc & ra & pb \\ rb & pc & qa \end{array} \right|$ is

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