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

Remember that in general AB \ne BA

Remember that in general AB \ne BA

## Software/Applets used on this page

## Glossary

### union

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

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AQA A-Level (UK - Pre-2017) | FP4 | Matrix algebra | The basics |

AQA AS Further Maths 2017 | Pure Maths | Matrix Determinants and Inverses | Matrix Equations |

AQA AS/A2 Further Maths 2017 | Pure Maths | Matrix Determinants and Inverses | Matrix Equations |

CBSE XII (India) | Algebra | Matrices | Types, zero, identity, symmetric and skew symmetric |

CCEA A-Level (NI) | FP1 | Matrix algebra | The basics |

Edexcel A-Level (UK - Pre-2017) | FP1 | Matrix algebra | The basics |

Edexcel AS Further Maths 2017 | Core Pure Maths | Matrices | Matrix Equations |

Edexcel AS/A2 Further Maths 2017 | Core Pure Maths | Matrices | Matrix Equations |

Methods (UK) | M5 | Matrix algebra | The basics |

OCR A-Level (UK - Pre-2017) | FP1 | Matrix algebra | The basics |

OCR AS Further Maths 2017 | Pure Core | Determinants, Inverses and Equations | Matrix Equations |

OCR MEI AS Further Maths 2017 | Core Pure A | Determinants and Inverses | Matrix Equations |

OCR-MEI A-Level (UK - Pre-2017) | FP1 | Matrix algebra | The basics |

Pre-Calculus (US) | E2 | Matrix algebra | The basics |

Scottish Advanced Highers | M3 | Matrix algebra | The basics |

Scottish (Highers + Advanced) | AM3 | Matrix algebra | The basics |

Universal (all site questions) | M | Matrix algebra | The basics |

WJEC A-Level (Wales) | FP1 | Matrix algebra | The basics |