Matrix Calculator

= 42 GoCalc

Add, subtract, and multiply matrices. Calculate determinant and transpose.Updated 2026-03-20

Frequently Asked Questions

How do I enter a matrix?

Separate columns with commas, rows with semicolons. E.g., 1,2;3,4 for a 2x2 matrix.

What operations are supported?

Addition, subtraction, multiplication, determinant, and transpose.

Is this free?

Yes, completely free with no signup.

How to Use

  1. Click Calculate to see the breakdown
  2. Review the step-by-step explanation
  3. Save or print the results
  4. Fill in the required values above

FAQ

How is the result calculated?

Uses standard mathematical formulas widely accepted in the field. The formula is shown with each result.

Can I compare different scenarios?

Adjust the inputs and recalculate to compare different scenarios side by side.

Are results suitable for professional use?

Provides accurate results based on standard formulas. For critical decisions, consult a professional.

What if I get an unexpected result?

Double-check your input values and units. The tool validates inputs and shows error messages.

What matrix operations are supported?

Our calculator supports addition, subtraction, multiplication, determinant, inverse, transpose, eigenvalues, and row echelon form for matrices up to 10x10.

Can I calculate the determinant of a 4x4 matrix?

Yes, our tool calculates determinants for matrices of any size up to 10x10 using cofactor expansion and LU decomposition methods.

How do I find the inverse of a matrix?

Enter your matrix, select "Inverse" operation, and click Calculate. The tool uses Gauss-Jordan elimination. Note: only square matrices with non-zero determinants have inverses.

What is row echelon form?

Row echelon form (REF) is a simplified form of a matrix where each leading entry is to the right of the one above it, and all entries below leading entries are zero. It is used to solve systems of linear equations.

Can I use fractions in the matrix?

Yes, you can enter fractions (like 1/3 or 2/5) and decimal numbers. Results can be displayed in both fraction and decimal format.

Rate this tool

β˜† β˜† β˜† β˜† β˜†

Found a bug? Let us know

Matrix Operations Explained

OperationDescriptionRequirements
Addition / SubtractionAdd or subtract corresponding elementsSame dimensions
MultiplicationDot product of rows and columnsCols of A = Rows of B
DeterminantScalar value from square matrixSquare matrix only
InverseMatrix that produces identity when multipliedSquare, non-singular
TransposeSwap rows and columnsAny matrix
EigenvaluesScalar values satisfying Av = lvSquare matrix only
Row Echelon FormTriangular form for solving equationsAny matrix

Common Matrix Sizes

Matrix Calculator Use Cases

Students

Verify homework answers, understand step-by-step solutions for linear algebra courses.

Engineers

Solve systems of equations, structural analysis, circuit analysis, control systems.

Data Scientists

Quick matrix operations for prototyping, covariance matrices, PCA calculations.

Game Developers

3D transformations, rotation matrices, projection matrices for rendering.