Matrix Calculator

A matrix is a rectangular table of numbers arranged in rows and columns. Matrix operations (addition, multiplication, determinant) are fundamental in linear algebra, 3D graphics, machine learning and solving systems of linear equations.

The determinant is a scalar value associated with a square matrix. If det(A) ≠ 0, the matrix is invertible. The det of a 2×2: ad-bc. For a 3×3 use Sarrus rule or cofactor expansion.

A×B ≠ B×A in general, because the row×column product changes result based on order. Matrix addition is commutative (A+B = B+A). This property is fundamental in physics (3D rotations) and computer graphics.

Addition, subtraction, the product of two matrices and the determinant of a single one. The result updates as soon as a coefficient changes, so you can watch what each edit does to the answer.

Addition and subtraction need matrices of the same size, because they work element by element. The product has a different rule: the columns of the first must match the rows of the second.

Because each entry of the result comes from a row of the first matrix meeting a column of the second. Swapping the order pairs different rows and columns, so A times B and B times A are generally different matrices.

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