Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare this as read-only, idempotent, open-world, and non-destructive. The description adds useful behavioral context beyond annotations: rejection of invalid determinants, per-call payment cost, and the HTTPS endpoint alias.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is front-loaded with the core operation and determinant constraint, followed by a concrete example and then payment/endpoint details. Every sentence adds relevant information without unnecessary verbosity.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple read-only math tool with one parameter and no output schema, the description is largely complete: it states the domain, gives an example, explains rejection behavior, and mentions cost/endpoint. The main remaining gap is that the exact matrix layout is only implied by the example.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate for the single matrix parameter. The example [1, 1, 0, 1] -> [1, -1, 0, 1] helps clarify the expected four-integer representation, but it does not explicitly define row-major ordering or fully explain the parameter semantics.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description gives a specific verb-resource pair: computes the inverse of a 2x2 integer matrix, with the determinant restricted to 1 or -1. It is clear what the tool does, though it does not explicitly contrast itself with siblings such as sl2_det or matrix_ops.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

It states an important precondition and rejection rule: the matrix determinant must be 1 or -1, otherwise the call is rejected. However, it does not explicitly say when to use this instead of related sibling tools, so the usage guidance remains implicit.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.