Matrix Calculator
Add, subtract, multiply, transpose, determinant, inverse, power and scalar operations on matrices up to 6×6 with step-by-step work.
3×3 matrix
- C is 3×3. Cᵢⱼ = Σ Aᵢₖ × Bₖⱼ
What is Matrix Calculator?
A matrix calculator is an essential tool for students, engineers, and data scientists who work with linear algebra. Matrices are rectangular arrays of numbers used to represent systems of equations, transformations, and data structures across mathematics, physics, computer graphics, and machine learning.
This tool lets you add, subtract, and multiply matrices, compute the inverse of a square matrix, and find the determinant — all without manual row reduction or hand calculations. Supports matrices from 2x2 up to 6x6, covering the vast majority of textbook and real-world problems.
Matrix addition and subtraction are element-wise operations requiring identical dimensions. Matrix multiplication follows the row-by-column dot product rule and requires compatible dimensions. The determinant is a scalar value derived from a square matrix and tells you whether the matrix is invertible. The inverse exists only when the determinant is non-zero.
Whether you are solving a system of simultaneous equations, checking linear independence of vectors, or verifying hand calculations from a homework problem, this calculator gives instant, step-traceable results. All computation happens in your browser — your data stays private and there is no server round-trip.
How to Use Matrix Calculator
- Set matrix dimensions
Choose the number of rows and columns (up to 6x6) for each matrix you want to work with.
- Enter matrix values
Fill in the cells of each matrix. You can tab between fields for fast entry.
- Choose an operation
Select add, subtract, multiply, inverse, or determinant from the operation menu.
- Copy the result
View the resulting matrix or scalar instantly and copy it to use in your work.
Key Benefits
All operations compute in real time as soon as you select an operation — no submit button needed.
Covers addition, subtraction, multiplication, inverse, and determinant in one place.
All calculations run locally in your browser. No matrix data is sent to any server.
Correctly validates dimension compatibility and warns you when an operation is undefined.
Frequently Asked Questions
A matrix can only be inverted if it is square (same number of rows and columns) and its determinant is not zero. A zero determinant means the matrix is singular and has no inverse.
The determinant is a scalar value that summarises key properties of a square matrix. If it is zero, the matrix is singular (not invertible). Its absolute value represents how much the transformation scales area or volume.
Yes. Matrix multiplication is not commutative — A times B generally does not equal B times A. Make sure you select the correct order for your use case.
The calculator supports matrices up to 6x6, which covers most linear algebra textbook problems and many real-world engineering scenarios.
Related Tools
Matrix Operations Reference
Matrix Multiplication
For A×B, the number of columns in A must equal the number of rows in B. The result C has dimensions (rows of A) × (cols of B). Each entry Cᵢⱼ = Σ Aᵢₖ × Bₖⱼ.
Determinant
The determinant is a scalar value for square matrices. A determinant of zero means the matrix is singular (not invertible). Computed via Laplace expansion — efficient for matrices up to 6×6.
Matrix Inverse
The inverse A⁻¹ satisfies A × A⁻¹ = I (identity matrix). Only square, non-singular matrices have an inverse. Computed via Gauss-Jordan elimination on the augmented matrix [A|I].