चक्रीय शिफ्ट करने पर अदिश त्रिक गुणनफल (a, b, c) का मान नहीं बदलता। :
Swapping the positions of the operators without re-ordering the operands leaves the triple product unchanged. This follows from the preceding property and the commutative property of the dot product.
Swapping any two of the three operands negates the triple product. This follows from the circular-shift property and the anticommutativity of the cross product.
The scalar triple product can also be understood as the determinant of the 3×3 matrix (thus also its inverse) having the three vectors either as its rows or its columns (a matrix has the same determinant as its transpose):
If the scalar triple product is equal to zero, then the three vectors a, b, and c are coplanar, since the parallelepiped defined by them would be flat and have no volume.
If any two vectors in the triple scalar product are equal, then its value is zero:
The simple product of two triple products (or the square of a triple product), may be expanded in terms of dot products:
This restates in vector notation that the product of the determinants of two 3×3 matrices equals the determinant of their matrix product.