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

Annotations already declare readOnly, idempotent, non-destructive, closed-world behavior, so the safety profile is covered. The description adds real value beyond that by disclosing the return contract: the inverse plus verification, or null with singular=true when the matrix is not invertible.

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?

Three sentences, front-loaded with the core action and method, then usage, then return behavior. The middle enumeration of Gauss-Jordan steps is slightly dense but every clause carries information; nothing is padding.

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?

With no output schema, the description carries the return-value burden and does so fully: it names the inverse, the verification, and the singular fallback. Combined with the annotations, an agent has enough to call and interpret the tool correctly.

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?

There is a single parameter with 100% schema description coverage, so the schema already documents it. The description restates the "square" constraint but adds no format details (e.g. whether strings accept fractions like "1/3"), so it stays at the baseline.

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?

States a specific verb and resource ("Find an exact inverse of a square matrix") plus the method (Gauss-Jordan elimination), which clearly separates it from the calculator-style siblings matrix_multiply, matrix_determinant, and matrix_transpose.

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?

The "Use for inverse questions needing..." sentence gives concrete triggers (exact fractions, augmented matrices, row swaps, verification). It offers no explicit exclusions or alternative routing, but the sibling tools perform entirely different operations, so there is little ambiguity to resolve.

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