# The determinant of a 3 x 3 matrix (General & Shortcut Method)

### The determinant of a 3 x 3 matrix (General & Shortcut Method)

In this section, we will learn the two different methods in finding the determinant of a 3 x 3 matrix. Instead of memorizing the formula directly, we can use these two methods to compute the determinant. The first method is the general method. This method requires you to look at the first three entries of the matrix. For each entry, you want to multiply that entry by the determinant of a 2 x 2 matrix that is not in that entry's row or column. Note that you have to put a negative sign on the second entry. Then you add everything up, and that will be the determinant of the 3 x 3 matrix. The second method is a shortcut. Watch the video to have a clear explanation of how it works.

#### Lessons

Let the matrix , where $a, b, c, d, e, f, g,$ and $i$ are all numbers.
We denote the determinant of $X$ to be det$(X)$. To find the determinant of a 3 x 3 matrix, we compute the following:
$a(ei-fh)-b(di-fg)+c(dh-ge)$

This formula is very ugly. Instead, use the General Method or the Shortcut Method. Learn to do this by watching the video!
• Introduction
The determinant of a 3 x 3 matrix Overview
a)
The General Method

b)
The Shortcut Method

• 1.
Finding the Determinant using the General Method
You are given that . Find the determinant using the General Method.

• 2.
You are given that . Find the determinant using the General Method.

• 3.
You are given that . Find the determinant using the General Method.

• 4.
Finding the Determinant using Shortcut Method
You are given that . Find the determinant using the Shortcut Method

• 5.
You are given that . Find the determinant using the Shortcut Method

• 6.
You are given that . Find the determinant using the Shortcut Method