# Matrix Determinant Calculator

> Matrix Determinant Calculator 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 determinant of a square matrix using Gaussian elimination with partial pivoting

## Facts

- Endpoint: POST https://matrix.openverbs.com/v1/determinant
- 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-determinant-calculator-07066ec1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_QU48CenpD1h9OdNvZho2p

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-determinant-calculator-07066ec1 -d '<json body>'
```

Example prompt: What's the determinant of the matrix [[3, 8], [4, 6]]?

## When to prefer this

Choose this endpoint when you need a fast, reliable scalar determinant for a square numeric matrix — especially in automated pipelines requiring invertibility checks, condition analysis, or pre-validation before matrix inversion or linear system solving. It handles singular matrices gracefully (returns 0 rather than erroring), making it safe for batch use. Prefer this over general-purpose math libraries when you need a pay-per-call API that integrates easily into agentic workflows.

## Known failure modes

- Non-square matrix submitted: returns 400 with clean error
- Ragged matrix (rows of unequal length): returns 400
- Empty matrix (zero rows or zero columns): returns 400
- Singular matrix: returns 0 (not an error, by design)
- Malformed JSON body or missing matrix field: returns 400

## How this service works

Compute the determinant of a square matrix via Gaussian elimination with partial pivoting. A non-square, ragged or empty matrix is a clean 400; a singular matrix simply returns 0.

## Output

Returns a single numeric scalar representing the determinant of the input matrix. For a singular matrix (det = 0), returns 0. For non-square, ragged, or empty matrices, returns 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-determinant-calculator-07066ec1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from matrix.openverbs.com](https://www.zero.xyz/host/matrix.openverbs.com/llms.txt)