Young Geniuses · Ages 13 to 14
Matrix Operations Fill-in
Add and multiply 2×2 matrices and fill in the resulting matrix. A Grade 8–9 algebra worksheet with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Matrix Operations Fill-in
Matrix Operations Fill-in introduces upper-secondary learners to matrices and the two core operations on them: addition and multiplication. Each question shows a pair of two-by-two matrices with an operation between them, and the student works out the resulting matrix and fills it in. Matrix addition combines corresponding entries, while matrix multiplication follows the row-by-column rule that students often find surprising at first; practising both builds a clear sense of how matrices behave. Matrices appear in the Grade 8 to 9 and early high-school curricula across the US, UK, Canada and Australia, and they are the language of transformations, simultaneous equations and a great deal of higher mathematics, computer graphics and data science. The matrices are shown in proper bracketed form so the layout matches how matrices are written everywhere else, and the entries are kept as small whole numbers so the arithmetic stays manageable and the focus is on the method. The five levels grow the entries and mix addition with multiplication. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key giving the full resulting matrix for each question. There is no advertising and no sign-up.
Common questions
- Which operations are covered?
- Adding 2×2 matrices entry by entry and multiplying them with the row-by-column rule.
- What grade is this for?
- Grade 8 to Grade 9 learners aged 13 to 14.
- Is an answer key included?
- Yes, every level gives the full resulting matrix.
A hand for grown-ups
- Before you start
- Find a calm few minutes with no rush. Let your child know it is fine to find some of it tricky — that is what practice is for.
- While they work
- Sit nearby but let them lead. If they get stuck, ask "what could you try?" rather than giving the answer — the thinking is the point.
- Afterwards
- Ask them to show you one they found easy and one they found hard. Praise the effort on the hard one, not just the right answers.
- Watch out for
- Rushing. If answers come too fast and wrong, slow the pace down together rather than pushing for more.
- Away from the screen
- Look for the same maths in everyday life — counting stairs, sharing snacks, spotting shapes on a walk.
Where to go next
Chosen by the skills this activity practises.