Definition:Determinant/Matrix/Order 3/Einstein Summation Convention

Definition
The determinant of a square matrix of order $3$ $\mathbf A$ can be expressed using the summation convention as:


 * $\map \det {\mathbf A} = \dfrac 1 6 \map \sgn {i, j, k} \map \sgn {r, s, t} a_{i r} a_{j s} a_{k t}$

Note that there are $6$ indices which appear twice, and so $6$ summations are assumed.