The value of the determinant \begin{vmatrix}a&b&c\\ l&m&n\\ p&q&r\end{vmatrix} is equal to

Explanation

Let the given determinant be \Delta. Interchanging rows multiplies the determinant by -1. Applying two successive row swaps cyclically (R_1 \leftrightarrow R_2 and then R_2 \leftrightarrow R_3) multiplies the determinant by (-1) \times (-1) = 1, shifting the rows to yield \begin{vmatrix}p&q&r\\ a&b&c\\ l&m&n\end{vmatrix}.

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