In this tutorial, we see two methods to calculate the determinant of 3×3 matrix. In the first sample, we see how to use first row expansion. In the second sample, we see a nice and simple method to construct the same formula with the help of Sarrus rule..

Calculate Determinant of 3×3 Matrix Using Row Expansion

You can calculate the Determinant of 3×3 Matrix using row expansion or column expansion. Let’s see how to calculate the determinant using first row expansion.

As you can see, using this method you has more 3 steps. Now you need to calculate 3 Determinants of 2×2 Matrix. In the next method, we see a simple way to calculate determinant of 3×3 matrix.

Calculate Determinant of 3×3 Matrix using the Sarrus rule

The Sarrus rule is simple method to calculate determinant of 3×3. It allows to construct the above formula of the first row expansion we see above. However, It is much simpler to remember. Let’s see the Sarrus rule in action:

Please note that Sarrus rule is unique to 3×3 Matrix. It can not be used for other Matrix.

With the Sarrus rule, you can construct the same formula we get when we use the first-row expansion we see above. In other words, you will get the same formula in both methods. The significant advantage of using the Sarrus rule over the first-row expansion method for calculating the determinant of 3×3 Matrix is the easy way to remember and construct the calculation.

Summery

We see two methods to calculate determinant of 3×3 Matrix. Using those methods, we can easily find the determinant of 3×3 Matrix. The first method – row expansion – works for any Matrix. However, the second method – Sarrus rule – is unique to 3×3 Matrix and much easier to remember and is less error prone.