Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, transpose, determinant, inverse, and adjoint. Supports 2x2 to 5x5 matrices with step-by-step solutions. All calculations happen locally — nothing leaves your browser.
How to Use the Matrix Calculator
- Select matrix size — choose from 2×2 to 5×5 matrices.
- Choose an operation — select add, subtract, multiply, scalar multiply, transpose, determinant, inverse, or adjoint.
- Fill in the matrices — enter values in Matrix A (and Matrix B if required).
- Click Calculate — view the result with step-by-step solution.
- Use additional features — generate identity matrices, swap matrices, or view eigenvalues.
Why Use a Matrix Calculator?
Matrices are fundamental to linear algebra, computer graphics, physics simulations, and data science. Manually computing matrix operations is error-prone and time-consuming, especially for larger matrices.
This calculator provides instant results with step-by-step explanations, making it ideal for students learning linear algebra, engineers solving systems of equations, and anyone working with data transformations.
Frequently Asked Questions
For matrix multiplication A × B, the number of columns in A must equal the number of rows in B. For square matrices of the same size, multiplication is always defined but is generally not commutative (A × B ≠ B × A).
A matrix is not invertible (singular) when its determinant is zero. This means the matrix maps space to a lower dimension and cannot be reversed.
Eigenvalues are scalars λ such that Av = λv for some non-zero vector v (the eigenvector). They reveal important properties about the matrix's behavior, such as scaling factors along principal axes.
Use Cases
Linear Algebra Homework
Multiply matrices and verify homework solutions with step-by-step explanations.
Finding Matrix Determinants
Calculate determinants of 2x2 to 5x5 matrices to test invertibility and solve equations.
Solving Systems of Equations
Use matrix operations to solve systems of linear equations efficiently and accurately.
Computing Matrix Inverses
Find inverse matrices to solve equations and verify mathematical proofs.
Matrix Transformations
Perform matrix transformations for computer graphics, physics, and data science applications.