# Matrix Inverse via Gauss-Jordan Elimination

> Matrix Inverse via Gauss-Jordan Elimination is a paid API for AI agents from matrix.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-14).

Computes the inverse of a square matrix using Gauss-Jordan elimination, returning the inverse matrix or indicating non-invertibility if the matrix is singular.

## Facts

- Endpoint: POST https://matrix.openverbs.com/v1/inverse
- Price: $0.004/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/matrix-inverse-via-gauss-jordan-elimination-ad7cd03d
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ska46QkXYn2pYpawY-2Il

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability matrix-inverse-via-gauss-jordan-elimination-ad7cd03d -d '<json body>'
```

Example prompt: Can you find the inverse of this 3×3 matrix: [[2, 1, 0], [1, 3, 1], [0, 1, 2]]? If it turns out to be singular, just let me know it's not invertible.

## When to prefer this

Use this endpoint when you need a numerically computed matrix inverse for a square matrix and want clean handling of singular cases without exceptions — ideal when you need to know whether a matrix is invertible as part of your logic, not just the inverse value itself. Prefer this over general linear solvers when the explicit inverse (not just a solution to Ax=b) is required.

## Known failure modes

- 400 error if matrix is non-square (rows ≠ columns)
- 400 error if matrix rows have different lengths (ragged matrix)
- 400 error if the matrix or its rows are empty
- Successful response with invertible:false and inverse:null for singular matrices (determinant = 0)
- 402 Payment Required if x402 payment is not provided

## How this service works

Invert a square matrix via Gauss-Jordan elimination. A non-square, ragged or empty matrix is a clean 400. A singular (non-invertible) matrix is NOT an error — it returns a successful { invertible:false, inverse:null }.

## Output

Returns a JSON object with an `invertible` boolean and an `inverse` field containing the n×n inverse matrix as a 2D array of numbers, or `null` if the matrix is singular. Non-square, ragged, or empty matrices return a 400 error.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "type": "object",
     "required": [
      "matrix"
     ],
     "properties": {
      "matrix": {
       "type": "array",
       "items": {
        "type": "array",
        "items": {
         "type": "number"
        },
        "minItems": 1
       },
       "minItems": 1,
       "description": "Square matrix (n×n)."
      }
     },
     "additionalProperties": false
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/matrix-inverse-via-gauss-jordan-elimination-ad7cd03d/health.json
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