Tutorial

Matrix
multiplication.

Four rounds, three quick lessons. You'll learn to read matrices, pair, multiply, and compute.

01 Pair and multiply 1×2 · 2×1

02 Add the products 2×2 · 2×1

03 Full multiplication 2×2 · 2×2

04 Mix and finish two problems · type the result

Matrix
sizes.

A matrix is named by its dimensions — rows × columns. Some sizes have special names. Scroll through a few.

Square matrix n × n Same number of rows and columns. 2×2 and 3×3 are square.

Row matrix 1 × n A single row. Like 1×2 or 1×4.

Column matrix n × 1 A single column. Like 2×1 or 3×1.

Quick check — what size is this matrix?

→

×

01 / 04 A 1×2 · B 2×1

Not every pair of matrices can be multiplied. Use this shortcut to know if you can.

(m × n) (p × q)

The inner dimensions must match.
When they do, the result is the outer pair: m × q.

Try a few:

If A and B can multiply, the answer takes the outer dimensions of the pair.

(m × n) (n × q) → m × q

Take the outer dimensions and you have the size of A · B.

Try predicting the result size for each pair of matrices.

Tutorial complete

You can read sizes, check compatibility, predict the result, and compute it.
That's matrix multiplication.