3 x 3 Determinants A Short Cut Method

```3 x 3 Determinants
A Short Cut Method
By
Dr. Julia Arnold
There are short cut methods of finding the determinant for
the 2x2 matrix and the 3x3 matrix. All square matrices of
size 4 and above must use the Cofactor and Minors method of
finding the determinant.
Dr. Burger, in his notes, has shown you the Cofactor method
for the 3x3 determinant and at the beginning of the notes he
shows the short cut method which may appear confusing.
I would like to show you an easier version of the short cut
method for finding determinants for a 3x3 matrix.
We will use the same example that is in the notes:
Example
2

3

 1
1
1
1
0

4

2 
Here is the easy way to arrive at that answer:
Step 1: Copy column 1 and 2 next to the matrix.
2

3

 1
1
1
1
02

4 3

2  1
1
1
1
Step 2: Beginning with 2, multiply the numbers on the diagonal (3
numbers only).
2

3

 1
1
1
1
02

4 3

2  1
1
To that add the product of the 3
numbers on the next diagonal.
1
1
2 ( 1 )2  1 ( 4 )( 1 )  0 (3 )( 1 )   4  4  0  0
And again, the product of the 3
numbers on the last diagonal.
Now beginning with the 1 in the upper right hand corner, we are
going to come back, multiplying the numbers on the diagonals.
We will also sum these and then subtract the answer from the
sum above.
2

3

 1
1
1
1
02

4 3

2  1
1
1
1 (3 )( 2 )  2 ( 4 )( 1 )  0 (  1 )( 1 )  6  8  0  14
1
Now subtract: 0 - 14 = - 14
```