left| begin{array}{ccc} 0 & p-q & p-r q-p & | vedclass

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(A) Let the given determinant be $D = \left| \begin{array}{ccc} 0 & p-q & p-r \ q-p & 0 & q-r \ r-p & r-q & 0 \end{array} ight|$.Notice that the m

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(A) Let the given determinant be $D = \left| \begin{array}{ccc} 0 & p-q & p-r \ q-p & 0 & q-r \ r-p & r-q & 0 \end{array} ight|$.Notice that the matrix $A = \begin{bmatrix} 0 & p-q & p-r \ q-p & 0 & q-r \ r-p & r-q & 0 \end{bmatrix}$ is a skew-symmetric matrix because $A^T = -A$.Specifically,the elements $a_{ij} = -a_{ji}$ for all $i, j$,and the diagonal elements are all $0$.The order of this matrix is $3 	imes 3$,which is an odd order.The determinant of a skew-symmetric matrix of odd order is always $0$.Therefore,$D = 0$.

$\left| \begin{array}{ccc} 0 & p-q & p-r \\ q-p & 0 & q-r \\ r-p & r-q & 0 \end{array} \right| = $

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