Perform matrix calculations quickly, accurately, and interactively. Calculate matrix operations including addition, subtraction, multiplication, determinant, inverse, transpose, rank, trace, scalar multiplication, matrix power, and linear equation systems.
a b c
d e f
g h i
Matrix A
Matrix B
Calculation Result
What is a Matrix?
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. Matrices are widely used in scientific computing, engineering, computer graphics, and various other fields.
Rows and Columns: The horizontal and vertical lines of entries in a matrix.
Square Matrix: A matrix with the same number of rows and columns (n × n).
Identity Matrix: A square matrix with 1s on the main diagonal and 0s elsewhere.
Common Matrix Operations
Addition & Subtraction
Requires matrices to have the exact same dimensions. Corresponding elements are added or subtracted.
Multiplication
Requires the number of columns in the first matrix to equal the number of rows in the second matrix.
Determinant
A scalar value that can be computed from the elements of a square matrix. Used to find the inverse.
Inverse
A matrix that, when multiplied by the original matrix, yields the identity matrix. Only non-singular square matrices have inverses.
Matrix Formulas
Addition
Cij = Aij + Bij
Multiplication
Cij = Σ AikBkj
Transpose
(AT)ij = Aji
2×2 Determinant
det(A) = ad − bc
FAQ
An online tool that allows you to easily perform complex mathematical operations on matrices, such as finding the determinant, inverse, or solving systems of linear equations.
Yes, but only if the number of columns in the first matrix exactly matches the number of rows in the second matrix.
Yes! Select 'Solve Linear System (Ax = b)' from the operations dropdown. Enter your coefficient matrix in Matrix A, and your constant vector in the first column of Matrix B.
Yes, all calculations are performed locally on your device using client-side JavaScript, ensuring fast performance and data privacy. No data is sent to a server.