The determinant of a 2 x 2 matrix A = \pmatrix{ a & b \cr c & d } is \det(A) = ad-bc .

The inverse of A is A^{-1} = \displaystyle \frac{1}{ad-bc} \pmatrix{ d & -b \cr -c & a }

If the determinant is zero (ie., the matrix is singular) then the matrix does not have an inverse.

The inverse of A is A^{-1} = \displaystyle \frac{1}{ad-bc} \pmatrix{ d & -b \cr -c & a }

If the determinant is zero (ie., the matrix is singular) then the matrix does not have an inverse.

## Summary/Background

The inverse of a matrix does not exist if the determinant is zero. Matrices whose determinant is not zero are called non-singular. Otherwise they are singular. To find the inverse of a 2x2 matrix:

- interchange the elements in the leading diagonal
- change the sign of the other two elements
- divide by the determinant

## Software/Applets used on this page

## Glossary

### matrix

a rectangular or square grid of numbers.

### non-singular

A matrix whose determinant is non-zero.

### union

The union of two sets A and B is the set containing all the elements of A and B.