Matrix Multiplication Calculator

Solve cᵢⱼ = Σₖ aᵢₖ·bₖⱼ (row i · column j) step by step — free matrix multiplication calculator with worked examples, real-world defaults and instant answers.

cᵢⱼ = Σₖ aᵢₖ·bₖⱼ (row i · column j)

Matrix A

Matrix B

[ 19  22 ]
[ 43  50 ]

A × B

1
Each result entry is one ROW of A dotted with one COLUMN of B:
c11 = (1)(5) + (2)(7) = 19 c12 = (1)(6) + (2)(8) = 22 c21 = (3)(5) + (4)(7) = 43 c22 = (3)(6) + (4)(8) = 50
2
Assemble:
[ 19 22 ] [ 43 50 ]

Matrix multiplication is composition of transformations, which is why order matters: AB ≠ BA in general (try swapping the defaults). The row-times-column rule exists so that (AB)x = A(Bx) — apply B first, then A.

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Matrix multiplication — row-by-column with each entry's dot product shown.

About Matrix Multiplication Calculator

The Matrix Multiplication Calculator solves cᵢⱼ = Σₖ aᵢₖ·bₖⱼ (row i · column j) for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. Matrix multiplication is composition of transformations, which is why order matters: AB ≠ BA in general (try swapping the defaults).

How to use Matrix Multiplication Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into cᵢⱼ = Σₖ aᵢₖ·bₖⱼ (row i · column j) and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Matrix Multiplication Calculator?

✓Solves cᵢⱼ = Σₖ aᵢₖ·bₖⱼ (row i · column j) instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Matrix Multiplication Calculator use?+

It uses cᵢⱼ = Σₖ aᵢₖ·bₖⱼ (row i · column j). The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Matrix Multiplication Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Matrix Multiplication Calculator on your website

Want Matrix Multiplication Calculatoron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.

Embed code

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