\begin{definition}[Definition:Determinant/Matrix/Order 3/Einstein Summation Convention]
The determinant of a square matrix of order $3$ $\mathbf A$ can be expressed using the Einstein 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.
\end{definition}