Matrix Calculator
Free matrix calculator. Perform matrix addition, subtraction, multiplication, transposition, determinant calculation, and inverse finding. Supports matrices up to 10x10 with step-by-step solutions.
Matrix A
Matrix B
What Is a Matrix?
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are used extensively in linear algebra, computer graphics, physics simulations, data science, and engineering. This calculator supports square matrices of sizes 2x2, 3x3, and 4x4.
Supported Operations
Addition and Subtraction: Add or subtract corresponding elements of two same-sized matrices. Multiplication: Multiply two matrices using the dot-product rule. Transpose: Flip a matrix over its main diagonal. Determinant: Compute the scalar value that describes certain properties of a square matrix. Scalar Multiplication: Multiply every element of a matrix by a constant.
Frequently Asked Questions
What is matrix multiplication?
Matrix multiplication takes two matrices and produces a new matrix. The element in row i, column j of the result is computed by taking the dot product of row i of the first matrix and column j of the second matrix. Note that matrix multiplication is not commutative: A x B does not always equal B x A.
What does the determinant tell us?
The determinant of a square matrix is a single number that encodes important properties. If the determinant is zero, the matrix is singular (non-invertible). The absolute value of the determinant represents the scaling factor for area (2D) or volume (3D) transformations.