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

Annotations already declare readOnly, non-destructive, closed-world behavior, so the safety profile is covered. The description's only additional signal is the supported size range (2×2 and larger), which is useful context, but it says nothing about failure behavior for non-square or malformed 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?

A single tight sentence with no filler, and the most useful constraint (size range) is included inline. Nothing is redundant, though there is little structure to speak of.

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 and annotations carrying return values and safety, the description only needs to nail input expectations. It partially does (square, size range) but leaves the row/array format and non-square handling unstated, which is the main thing an agent could get wrong.

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 coverage is 100%, so the single parameter is already documented as 'Square matrix.' The description adds the supported size range, but does not clarify the input shape (nested rows vs flat array), which matters given the schema's example is a 2D array while its item type is number.

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 exact operation (determinant) and the resource (square matrix), which cleanly separates it from siblings like calculator_matrix_inverse, calculator_rank, and calculator_transpose. The only shortfall is the noun-phrase phrasing rather than an explicit verb, but intent is unambiguous.

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?

No guidance on when to prefer this tool over alternatives — e.g., that a non-zero determinant implies invertibility and points to calculator_matrix_inverse — and no prerequisites or exclusions stated. Usage is only implied by the tool name.

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