Matrix Calculator
Add, subtract, multiply matrices. Find determinant, inverse, and transpose for 2×2 and 3×3 matrices.
Matrix A
Matrix B
About Matrix Calculator
Matrices are rectangular arrays of numbers used to represent linear transformations, systems of equations, and more. A 2×2 matrix has 2 rows and 2 columns; a 3×3 has 3 of each. Matrix addition and subtraction operate element-by-element. Multiplication follows the dot-product rule: element R[i][j] equals the dot product of row i of A with column j of B.
The determinant of a matrix encodes how it scales area (2D) or volume (3D). A non-zero determinant means the matrix is invertible — its inverse reverses the transformation. For a 2×2 matrix [[a,b],[c,d]], det = ad − bc, and the inverse is (1/det) × [[d,−b],[−c,a]]. The transpose swaps rows and columns: A^T[i][j] = A[j][i].
Matrices are central to linear algebra, computer graphics, machine learning, and physics simulations. Related tools: the Standard Deviation Calculator uses matrix-like data operations, and the Probability Calculator uses matrix methods for Markov chains.
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For a related calculation, use Standard Deviation Calculator to calculate population and sample standard deviation, variance, mean, and full descriptive stats from a dataset. Alternatively, use Random Number Generator to generate random numbers within a specified range for games, simulations, and more.
For the underlying method, read Matrix Operations Explained Simply: Addition, Multiplication, and the Determinant.