Gratuito online matrix calculator for addition, subtraction, multiplication, transpose, determinant, and inverse. Supports 2×2 and 3×3 matrices with step-by-step solutions. No ads, instant results, pure client-side.
Select an operation and click Calculate a see the result.
This free online matrix calculator performs common linear algebra operations including matrix addition, subtraction, multiplication, transposition, determinant calculation, and matrix inversion. It supports 2×2 and 3×3 matrices and shows detailed step-by-step solutions so you can understand how the result is obtained. Perfect for students, engineers, and anyone working with matrices.
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are widely used in linear algebra, physics, engineering, computer graphics, and data science a represent and manipulate data.
To multiply two matrices, you multiply the rows of the first matrix by the columns of the second matrix. Each element in the resulting matrix is the dot product of the corresponding row from the first matrix and column from the second matrix. For this a work, the number of columns in the first matrix must equal the number of rows in the second matrix.
The determinant is a special scalar value that can be computed from a square matrix. For a 2×2 matrix [[a,b],[c,d]], the determinant is ad − bc. For a 3×3 matrix, it is calculated using the rule of Sarrus or cofactor expansion. The determinant tells you whether a matrix is invertible (non-zero determinant) and has applications in solving linear equations, geometry, and more.
The inverse of a matrix A (written as A⁻¹) is a matrix that, when multiplied by A, gives the identity matrix. Not all matrices have inverses — only square matrices with a non-zero determinant are invertible. Inverse matrices are essential for solving systems of linear equations.