# Matrix arithmetic and invariants

> ML Prep screening item.

- Stable ID: `math-la-01-matrix-invariants`
- Collection: screening
- Area: Mathematics
- Topic: Linear Algebra
- Origin: original
- Difficulty: easy
- Expected time: 4 minutes
- Skills: matrix-operations, inverse, determinant, trace, matrix-norms
- Item JSON: https://mlprep.iwase.dev/item/math-la-01-matrix-invariants.json

## Problem

Let
$$
A=\begin{bmatrix}1&2\\3&5\end{bmatrix},\qquad z=\begin{bmatrix}1\\-1\end{bmatrix}
$$
Compute $Az$, $\det(A)$, $\operatorname{tr}(A)$, $A^{-1}$, and the Frobenius norm $\|A\|_F$.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-la-01-matrix-invariants`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.