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# Documentation

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```linalg::adjoint(A)
```

## Description

linalg::adjoint(A) computes the adjoint Adj(A) of the n×n matrix A. The adjoint matrix satisfies the equation , where In is the n×n identity matrix.

The component ring of A must be of category Cat::CommutativeRing.

## Examples

### Example 1

We define a matrix over the rationals:

```MatQ := Dom::Matrix(Dom::Rational):
A := MatQ([[0, 2, 1], [2, 1, 0], [1, 0, 2]])```

Then the adjoint matrix of A is given by:

`Ad := linalg::adjoint(A)`

`A * Ad = det(A)*MatQ::identity(3)`

## Parameters

 A A square matrix of a domain of category Cat::Matrix

## Return Values

Matrix of the same domain type as A.

## Algorithms

The adjoint of a square matrix A is the matrix whose (i, j)-th entry is the (j, i)-th cofactor of A.

The (j, i)-th cofactor of A is defined by , where Aij is the submatrix of A obtained from A by deleting the i-th row and j-th column.