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

Annotations already declare readOnlyHint=true, destructiveHint=false, openWorldHint=false, so the safety profile is covered. The description adds a genuinely useful behavioral fact — failure on singular matrices — but says nothing about numeric precision, return shape, or handling of ill-conditioned input.

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?

Two short sentences with zero filler, leading with the operation and immediately following with the failure condition. Every clause earns its place.

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 an output schema covering return values and annotations covering safety, the description only needs to supply the domain caveat, which it does. It could go slightly further on numerical stability or non-square input handling, but the essentials are present for a simple one-parameter math tool.

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 at 100% schema coverage and the schema already states 'Square matrix.' The description's mention of squareness and invertibility does not add syntax or format detail beyond the schema, so the baseline of 3 applies.

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 the specific operation and resource (inverse of a square invertible matrix) rather than restating the name, so an agent knows exactly what is computed. It does not explicitly contrast itself with nearby siblings such as calculator_determinant, calculator_transpose, or calculator_matrix_multiply, which is why it stops short of a 5.

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?

Usage is only implied: the singular-matrix error hints at the precondition, but there is no guidance on when to pick this tool versus determinant/rank/transpose or how to chain it (e.g., multiply the result). The one exclusion it does give (fails on singular input) is stated as an error, not as routing advice.

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