# Manuals/calci/ADJ

**ADJ(Array)**

- is the set of values.

## Description

- This function shows the Adjoint of a given matrix.
- In , is the set of matrix values.
- Adjoint of a matrix is called adjugate, classical adjoint, or adjunct.Adjoint of a matrix formed by taking the transpose of the cofactor matrix of a given original Square matrix.
- Adjoint of matrix A is written by .
- The adjugate of A is the transpose of the cofactor matrix C of A, .
- Also adjoint of a matrix is defined by .
- The adjugate of 1x1 matrix is .
- The adjugate of 2x2 matrix is .
- Consider3x3 matrix .
- Its adjugate is the transpose of its cofactor matrix:

## Examples

1.adj([[10,12],[-14,21]])

21 | -12 |

14 | 10 |

2.adj([[4,5,8],[3,-6,-9],[10,-12,4]])

-132 | -116 | 2.9999999999999982 |

-102 | -64 | 60 |

24 | 98 | -39 |

3.adj([[5,-2,2,7],[1,0,0,3], [-3,1,5,0], [3,-1,-9,4]])

-12 | 76 | -60 | -36 | |

-56 | 207.99999999999997 | -81.99999999999999 | -57.99999999999999 | |

4 | 3.999999999999999 | -1.9999999999999998 | -10 | |

4 | 3.9999999999999982 | 20 | 12 |