# What is meant by the determinant of a matrix?

##### 3 Answers

Assuming that we have a square matrix, then the determinant of the matrix is the determinant with the same elements.

Eg if we have a

# bb(A) = ( (a,b), (c,d) ) #

The the associated determinant given by

# D = | bb(A) | = | (a,b), (c,d) | = ad-bc#

See below.

#### Explanation:

To extend on Steve's explanation, the determinant of a matrix tells you whether or not the matrix is invertible. If the determinant is 0, the matrix is not invertible.

For example, let

If we let

Additionally, the determinant is involved in computing the inverse of a matrix. Given a matrix

Also area / volume scale factor...

#### Explanation:

The determinant is also used as a area/volume scale factor,

If we have a

Then if a particular shape of area

Also