> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/sidef-lang/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/sidef-lang/programming_tasks/g/gauss-jordan_matrix_inversion.md).

# Gauss-Jordan matrix inversion

Uses the `rref(A)` function from [Reduced row echelon form](https://rosettacode.org/wiki/Reduced_row_echelon_form#Sidef).

```ruby
func gauss_jordan_invert (M) {

    var I = M.len.of {|i|
        M.len.of {|j|
            i == j ? 1 : 0
        }
    }

    var A = gather {
        ^M -> each {|i| take(M[i] + I[i]) }
    }

    rref(A).map { .last(M.len) }
}

var A = [
    [-1, -2, 3, 2],
    [-4, -1, 6, 2],
    [ 7, -8, 9, 1],
    [ 1, -2, 1, 3],
]

say gauss_jordan_invert(A).map {
    .map { "%6s" % .as_rat }.join("  ")
}.join("\n")
```

## Output:

```
-21/23   17/69  13/138   19/46
-38/23   15/23    1/23   15/23
-16/23   25/69  11/138    9/46
-13/23   16/69   -2/69   13/23
```