Determinant of a 3x3 Matrix

det(A) = a(ei + fh) - b(di - fg) + c(dh - eg)

det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

det(A) = a(ei - fh) + b(di + fg) - c(dh - eg)

det(A) = a(ei - fh) - b(di - fg) - c(dh - eg)

2

7

10

5

0

3

1

2

-42

7

10

-12

Determinant is negative

Determinant is 1

Determinant is 0

Determinant is undefined

-57

12

7

-45

The determinant being positive guarantees invertibility.

The determinant being zero guarantees invertibility.

The determinant of a matrix being non-zero indicates its invertibility.

The determinant being negative guarantees invertibility.

-5

77

0

12

The determinant of a matrix changes sign when its rows are interchanged.

The determinant of a matrix doubles when its rows are interchanged.

The determinant of a matrix becomes zero when its rows are interchanged.

The determinant of a matrix remains the same when its rows are interchanged.

-20

-25

7

10