Matrix Calculator
Perform matrix operations — add, multiply, transpose, find determinants and inverses.
Working with matrices
A matrix is a grid of numbers, and matrices have their own arithmetic that underlies much of higher mathematics, graphics and data science. This performs the common matrix operations, from addition and multiplication to determinants and inverses, handling the tedious calculation for you.
Enter your matrices and choose an operation.
Why matrix rules are their own thing
Matrix arithmetic has rules that surprise newcomers. Addition is straightforward, but multiplication is not element-by-element — it combines rows with columns in a specific way, and crucially the order matters, since multiplying two matrices one way can give a different result than the other, unlike ordinary numbers. The dimensions must also line up for multiplication to be defined at all. These rules exist because matrices represent transformations and systems, and matrix multiplication corresponds to combining them. That is why matrices are everywhere in computer graphics, where they rotate and scale objects, in solving systems of equations, and in the maths behind machine learning. The calculator handles the fiddly arithmetic so you can focus on what the operations mean.
Questions & answers
Is matrix multiplication done element by element?
No — it combines rows with columns in a specific way, and the order matters, so multiplying two matrices one way can differ from the other.
Where are matrices used?
Computer graphics for rotating and scaling, solving systems of equations, and the maths behind machine learning, among much else.
Is anything uploaded?
No. The calculation happens in your browser.