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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

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## 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-