Formula for the determinant of a 3-by-3 matrix.
Formula: For a $3 \times 3$ matrix (Sarrus rule):
$$\det\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = aei + bfg + cdh - ceg - bdi - afh$$
Formula: For a $3 \times 3$ matrix (Sarrus rule):
$$\det\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = aei + bfg + cdh - ceg - bdi - afh$$