Sarrus Rule is a neat shortcut for finding the determinant of a $3 \times 3$ matrix!

Here’s how it works:

1. Matrix Layout: First, look at this matrix:

$$\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}.$$

2. Diagonal Products: Next, find the sum of the diagonals that go down to the right. You will calculate:

   • $a \cdot e \cdot i + b \cdot f \cdot g + c \cdot d \cdot h$.

3. Anti-Diagonal Products: Now, subtract the sum of the diagonals that go up to the right. This means you will calculate:

   • $c \cdot e \cdot g + a \cdot f \cdot h + b \cdot d \cdot i$.

4. Final Calculation: To get the determinant, use this formula: $\text{det} = (a \cdot e \cdot i + b \cdot f \cdot g + c \cdot d \cdot h) - (c \cdot e \cdot g + a \cdot f \cdot h + b \cdot d \cdot i).$

By using Sarrus Rule, you'll find it easier to calculate determinants and enjoy learning about linear algebra even more!