Matrix Question Generator
Three matrix tasks, generated so the arithmetic stays exact. Inverses are the interesting case: a random two-by-two almost always has a fractional inverse, which turns an exercise about the method into an exercise about fractions. These are built from matrices whose determinant is 1 or −1, so the inverse has whole-number entries, and the check multiplies the two together and requires the identity exactly rather than approximately.
What this generator does
Generates two-by-two products, three-by-three determinants, or two-by-two inverses. Products also show the result of multiplying the other way round, since matrix multiplication does not commute and one instance makes that clearer than any amount of saying so.
How to use this tool
- Choose whether you want a multiplication, a determinant or an inverse.
- Work it out by hand.
- Reveal the answer, with the working written out.
- Seed a question to set the same one for someone else.
Understanding the controls
- Task
- Multiply two 2×2 matrices, take the determinant of a 3×3, or invert a 2×2. Each exercises a different part of the topic.
- Seed
- Reproduces the same matrices exactly from a word you pick.
- Show the answer
- Reveals the result along with the entry-by-entry working or the expansion.
Common use cases
- Practice at multiplication where the order matters and the instance shows it
- Determinant questions on three-by-three matrices with the sign pattern explained
- Inverse questions that do not collapse into fraction arithmetic
- Checking a hand calculation against a verified answer
- Producing the same matrices for a group from a seed
How this generator works
Products and determinants are computed directly from small whole-number entries. Inverse questions are constructed backwards: matrices are drawn until the determinant is 1 or −1, which guarantees an integral inverse. The check multiplies the matrix by its stated inverse and requires exactly the identity.
Randomness and fairness
The entries are random within the constraints each task needs; the answers are computed. Seeded questions reproduce and are therefore explicitly not cryptographically secure, and unseeded ones use the browser's cryptographically secure generator.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Sizes are fixed per task: two-by-two for products and inverses, three-by-three for determinants.
- Inverses are restricted to determinants of 1 and −1, which is a small and unrepresentative family.
- Eigenvalues, rank and row reduction are not among the tasks.
- Non-square and rectangular products are not generated.
- Questions are not stored; seed one you want to reissue.
Privacy and your data
Matrices and answers are generated in your browser and never leave it. Nothing persists after you close the page.
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