Matrix Multiplication Calculator
With the dimension check that decides whether it exists at all.
Work out Matrix Multiplication. With the dimension check that decides whether it exists at all. Free, with no account and nothing to download.
Rows separated by semicolons or new lines.
Product dimensions
2×2
19 22 · 43 50
Each entry of the product is the dot product of a row from the first matrix with a column from the second. That is why the inner dimensions must match: an m×n times an n×p gives an m×p, and the n has to be shared. Matrix multiplication is not commutative. AB and BA are usually different, and for non-square matrices one of them may not exist at all. That is not a quirk of the notation — it reflects that applying two transformations in a different order genuinely gives a different result.
How the Matrix Multiplication Calculator works
Paste two matrices for their product. Where the dimensions do not allow multiplication the page says exactly which pair failed to match, since that is the constraint people forget and the error is otherwise opaque.
Also known as: multiply two matrices calculator · matrix product calculator · matrix dimensions rule · how to multiply matrices
Frequently asked questions
When can two matrices be multiplied?
When the first matrix's column count equals the second's row count. An m×n times an n×p gives an m×p — the inner dimensions must match and then vanish.
How is each entry calculated?
As the dot product of a row from the first matrix with a column from the second: multiply corresponding entries and add. That is why the shared dimension has to match — it is the length of both.
Is matrix multiplication commutative?
No. AB and BA are usually different, and for non-square matrices one may not exist at all. That reflects something real: applying two transformations in a different order gives a different result.
What is the identity matrix?
A square matrix with ones on the diagonal and zeros elsewhere. Multiplying by it changes nothing, which makes it the matrix equivalent of 1.
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