Determinants

We can calculate the determinant for a 2×2 matrix as follows:

\begin{vmatrix} A \end{vmatrix} = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

We see three 2×2 determinant calculations done for a 3×3 dterminant calculation:

\begin{vmatrix} A \end{vmatrix} = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = a \begin{vmatrix} e & f \\ h & i \end{vmatrix} + b \begin{vmatrix} f & d \\ i & g \end{vmatrix} + c \begin{vmatrix} d & e \\ g & h \end{vmatrix}

= a(ei-fh) + b(fg-di) + c(dh-eg)

We do the middle term differently from the standard method. We do a “wrap-around” which puts the first column to the right of the third column, allowing us to follow the same pattern for all three additions and negating the need for the middle term to be a subtraction.