1. The determinant of a 3x3 matrix $A=\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}$ using Sarrus' rule is calculated as: $$\det(A) = aei + bfg + cdh - ceg - bdi - afh$$ 2. To apply Sarrus' method, write the first two columns of matrix $A$ again to the right of the matrix: $$\begin{bmatrix}a & b & c & a & b\\ d & e & f & d & e\\ g & h & i & g & h\end{bmatrix}$$ 3. Calculate the sum of the products of the diagonals going downwards to the right: $$a \times e \times i + b \times f \times g + c \times d \times h$$ 4. Calculate the sum of the products of the diagonals going upwards to the right: $$c \times e \times g + b \times d \times i + a \times f \times h$$ 5. The determinant is the difference between the two sums: $$\det(A) = (a e i + b f g + c d h) - (c e g + b d i + a f h)$$ This is the formula for the determinant of a 3x3 matrix by Sarrus' method.