Matrix Calculator

Online Matrix Calculator — Free and Advanced

Need to solve matrix operations quickly and accurately? Our
online matrix calculator is a free tool, with no
installation or registration required, designed for students, teachers,
and engineers who need instant results. It works directly in your browser,
both on desktop and mobile devices.

What can you calculate with this tool?

Unlike basic calculators, this tool covers complete linear algebra.
Below you’ll find all the available features:

Operations between two matrices (A and B)

Perform operations between two matrices up to 6×6:
matrix addition, matrix subtraction,
and matrix multiplication. The
Hadamard product (element-wise multiplication) and the
Kronecker product are also available, widely used in
tensor algebra and quantum computing.

Functions on a single matrix

For a given matrix, the calculator can compute the
determinant, trace,
rank, and Frobenius norm.
It also calculates the transpose,
inverse matrix, cofactor matrix,
and adjugate matrix. For more advanced operations,
it includes Reduced Row Echelon Form (RREF) with
step-by-step elimination, LU decomposition,
matrix powers (Aⁿ), and
scalar multiplication.

Solving systems of linear equations (Ax = b)

Enter the coefficient matrix A and vector b to solve the system
Ax = b using Gaussian elimination with partial
pivoting. The calculator displays the complete solution,
each step of the process, and the residual verification ‖Ax − b‖,
ensuring the result is correct.

Eigenvalues and eigenvectors calculation

Obtain the eigenvalues and
eigenvectors of square matrices of size
2×2, 3×3, and 4×4. For 2×2 matrices, the
characteristic polynomial is solved exactly;
for larger matrices, the QR iteration method
is applied. The discriminant and related properties are also shown.

How to use the matrix calculator?

It’s very simple: choose the matrix size using the row and column
fields, enter the values directly into the grid, and press the
operation you need. Results appear instantly, with step-by-step
explanations whenever the operation allows it. You can clear the
matrices, load random values, or generate an identity matrix with
a single click. The history tab stores the most
recent operations performed during your session.

Who is this calculator for?

It’s ideal for linear algebra, vector calculus,
and multivariate statistics students; for engineers working with
systems of equations or linear transformations; and for teachers
who want to display results and steps in class. It’s also an
excellent tool to verify hand-solved results.

Frequently Asked Questions

How do I calculate the determinant of a matrix online?
Enter the values into the grid, select the “Function(A)” tab, and click
“det(A)”. The result appears instantly along with an indicator of
whether the matrix is singular or not.

How do I invert a matrix online?
In the “Function(A)” tab, enter your square matrix and select “A⁻¹”.
If the matrix has a nonzero determinant, the calculator returns the
full inverse.

Can I solve systems of equations using matrices?
Yes. The “Systems Ax=b” tab is designed exactly for that. Enter the
coefficient matrix and the constant vector to obtain the solution
with all Gaussian elimination steps.

What is the maximum supported matrix size?
General operations accept matrices up to 6×6. Eigenvalue calculations
are available for 2×2, 3×3, and 4×4 matrices.