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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so safety is covered. The description adds genuinely useful context beyond that: the return payload includes factor pairs, products, and per-entry calculations, and inputs accept fractions as well as decimals. With no output schema present, this return-value disclosure is the value-add.

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 operation and its precondition, then output shape, then input flexibility. The middle clause about 'step-by-step row-by-column dot products' is mildly redundant with the return-value sentence but still adds usage framing rather than noise.

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 two-parameter math tool with no output schema, the description supplies the precondition, the accepted input formats, and the shape of the returned result, which is what an agent needs. It omits nothing critical, though it does not mention limits on matrix size or performance.

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 baseline is 3 and the schema already documents matrixA and matrixB. The description goes beyond it by clarifying that numeric entries may be passed as fractions or decimals, which is not evident from the string|number union in the schema.

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+resource (multiply matrix A by matrix B) and immediately scopes it with the compatibility rule (A's columns must equal B's rows). The operation is unambiguously distinct from sibling tools like matrix_add, matrix_transpose, and matrix_determinant, so an agent can select it without opening a schema.

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?

Gives a concrete precondition for use (column count of A equals row count of B) and clarifies that non-square matrices are supported, which is the main ambiguity for a multiply tool. It does not, however, explicitly route the agent away from or toward any named sibling, so it falls short of a 5.

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