For a matrix, for instance, like:
\begin{equation} \begin{bmatrix} a & b \\ c & d \end{bmatrix} \end{equation}
We wish to find the matrix’s determinant; we write it down as:
\begin{equation} \begin{vmatrix} a & b \\ c & d \end{vmatrix} \end{equation}
geometric interpretation of determinants
Geometrically, determinants are how matrices send a unit object after its mapping; i.e. how does it transform the area of a unit square.
determinants can be computed along any axes
You can pick any row or column as the “axes”, and expand the matrix along any direction