Main content

## Algebra (all content)

### Unit 20: Lesson 15

Determinants & inverses of large matrices- Determinant of a 3x3 matrix: standard method (1 of 2)
- Determinant of a 3x3 matrix: shortcut method (2 of 2)
- Determinant of a 3x3 matrix
- Inverting a 3x3 matrix using Gaussian elimination
- Inverting a 3x3 matrix using determinants Part 1: Matrix of minors and cofactor matrix
- Inverting a 3x3 matrix using determinants Part 2: Adjugate matrix
- Inverse of a 3x3 matrix

© 2022 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Determinant of a 3x3 matrix: shortcut method (2 of 2)

Sal shows a "shortcut" method for finding the determinant of a 3x3 matrix. Created by Sal Khan.

## Video transcript

As another hint, I will take the same matrix, matrix A and take its determinant again but I will do it using a different technique, either technique is valid so here we saying what is the determinant of the 3X3 Matrix A and we can is we can rewrite first two column so first column right over here we could rewrite it as 4 4 -2 and then the second column right over here we could rewrite it -1 5 0 and we could do is we could take the sum of the products of the first three top left bottom left diagonal, let me show you so the product of that that plus that plus that trying my best to draw this neatly and then from that subtract top right to bottom left diagonal so from that subtract let get a color I havent used subtract that and that and that sounds really confusing with all the diagonals i have drawn lets look at the blue ones first 4 times 5 times 0 4 times 5 times 0 plus -1 times 3 times -2 plus -1 times 3 times -2 let me put these in parenthesis plus 1 times 4 times 0 and then we gonna subtract all of these orange diagonal, we go from the top right to the bottom left so we gonna subtract we could do 1 times 5 times -2 1 times 5 times -2 and then we can subtract subtract 4 times 3 times 0 4 times 3 times 0 and then we can subtract -1 times 4 times 0 -1 times 4 times 0 and now we just evaluate this over here 4 times 5 times 0 is just 0 -1 times 3 times -2 is +6 so this is +6 1 times 4 times 0 is 0 once again and then we have 1 times 5 times -2 is -10 but we have this negative out here so it becomes a +10 then 4 times 3 times , well thats just going to be 0. and then we have -1 times 4 times 0, which is just 0 so we are left with +6 + 10 which is equal to +16