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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.

## 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:
1. interchange the elements in the leading diagonal
2. change the sign of the other two elements
3. divide by the determinant You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## 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.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP4Matrix algebraInverses-
AQA AS Further Maths 2017Pure MathsMatrix Determinants and InversesDeterminants and Inverses-
AQA AS/A2 Further Maths 2017Pure MathsMatrix Determinants and InversesDeterminants and Inverses-
CBSE XII (India)AlgebraMatricesInverse of matrices and proof of uniqueness, if it exists.-
CCEA A-Level (NI)FP1Matrix algebraInverses-
Edexcel A-Level (UK - Pre-2017)FP1Matrix algebraInverses-
Edexcel AS Further Maths 2017Core Pure MathsMatricesDeterminants and Inverses-
Edexcel AS/A2 Further Maths 2017Core Pure MathsMatricesDeterminants and Inverses-
Methods (UK)M5Matrix algebraInverses-
OCR A-Level (UK - Pre-2017)FP1Matrix algebraInverses-
OCR AS Further Maths 2017Pure CoreDeterminants, Inverses and EquationsDeterminants and Inverses-
OCR MEI AS Further Maths 2017Core Pure ADeterminants and InversesDeterminants and Inverses-
OCR-MEI A-Level (UK - Pre-2017)FP1Matrix algebraInverses-
Pre-Calculus (US)E2Matrix algebraInverses-