132. Determinants of nine digits. Nine positive digits can be arranged in the form of a third-order determinant in 9! ways. Find the sum of all such determinants.
132. If we interchange two adjacent rows of a determinant, it will change its sign. If we permute the rows of a certain third-order determinant in all possible ways, we will obtain three positive and three negative determinants, equal to each other in absolute value. Consequently, our 9! determinants break down into $\frac{9!}{6}$ groups, and the sum of the determinants within each such group is zero.

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[M . \text { M., 36, } 77 \text { (January 1963).] }
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