How to use

This tool brings the core small-matrix operations together. Use 2×2 or 3×3 matrices for addition, subtraction and multiplication, or calculate determinant, transpose and inverse when mathematically defined.

Choose 2×2 or 3×3.
Choose the operation.
Enter matrix A and matrix B for binary operations.
Calculate and review the result or a validity message.

How it is calculated

(AB)ᵢⱼ=Σₖaᵢₖbₖⱼ; det(A); A⁻¹ when det(A)≠0

Example

For [[4,7],[2,6]], the determinant is 10 and the inverse is [[0.6,-0.7],[-0.2,0.4]].

Important notes

An inverse exists only for a square nonsingular matrix. Matrix multiplication is generally not commutative: A×B may differ from B×A.

Frequently asked questions

When does an inverse not exist?

When the determinant is zero or numerically indistinguishable from zero.

Is A×B equal to B×A?

Not in general; order matters.

Is 3×3 supported?

Yes for the operations shown in the calculator.

Is this calculator free?

Yes. It is free to use and requires no account.

Matrix Calculator