The Matrix Calculator adds, subtracts and multiplies matrices and finds the transpose, determinant, inverse and powers of a matrix.
| AB | 1 2 3 4 | 5 6 7 8 | 2 6 4 8 | 3 1 1 2 |
A matrix is a rectangular grid of numbers arranged in rows and columns. Matrices represent systems of linear equations, geometric transformations, networks, images and data tables, and are central to engineering, physics, computer graphics and machine learning.
Addition and subtraction work element by element and need equal sizes. Multiplication AB needs the columns of A to equal the rows of B; each entry is the dot product of a row of A and a column of B. Matrix multiplication is not commutative: AB is usually not BA.
The determinant of a square matrix is a single number showing how the matrix scales area or volume; for 2 × 2, |A| = ad − bc. A matrix has an inverse A⁻¹ (with AA⁻¹ = I) only if its determinant is not zero. Inverses solve systems: if Ax = b then x = A⁻¹b.
What is the identity matrix? Ones on the diagonal, zeros elsewhere; multiplying by it changes nothing.
What is the transpose? Rows become columns.
How do I enter fractions? Use decimals.