Determine the determinant of
\begin{pmatrix}A & B & C \\
R & D & E \\
S & F & G
\end{pmatrix}.
\det =
det
For a 3 \times 3 - matrix (and only in this case) the determinant is given by the rule of Sarrus,
this yields \det = det.
If there are some zeros in the matrix, Laplace expansion along a row or column is a (more) suitable method.