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Kordu Tools
Math & Numbers Runs in browser Updated 30 Mar 2026

Matrix Calculator

Perform matrix addition, subtraction, multiplication, determinant, inverse, transpose, and row echelon form on matrices up to 6×6.

Matrix A
3x3
rows
3
cols
Scalar\u00D7 A

Determinant

0

Step-by-Step

Expanding along row 1 of 3x3 matrix

det([0,0; 0,0]) = 0*0 - 0*0 = 0

+ 0 * M(1,1) = + 0 * 0 = 0

det([0,0; 0,0]) = 0*0 - 0*0 = 0

- 0 * M(1,2) = - 0 * 0 = 0

det([0,0; 0,0]) = 0*0 - 0*0 = 0

+ 0 * M(1,3) = + 0 * 0 = 0

Determinant = 0

2 × A

Key Formulae

det(A) = cofactor expansion along any row or column

A⁻¹ = [A|I] row-reduced to [I|A⁻¹] (exists only if det(A) ≠ 0)

(AB)ᵢⱼ = sum of A(i,k) * B(k,j) for k = 1..n
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How to use Matrix Calculator

  1. Set the matrix dimensions

    Use the +/− row and column buttons to set the matrix size from 2×2 up to 6×6.

  2. Enter matrix values

    Click each cell and type values. Tab between cells. Or paste tab- or comma-separated data from a spreadsheet.

  3. Choose an operation

    Select determinant, inverse, transpose, row echelon form, or another operation. For two-matrix operations, toggle two-matrix mode and fill in the second matrix.

  4. View the result

    The result matrix or scalar appears instantly with the formula used.

  5. Expand step-by-step working

    For determinant and inverse, click 'Show steps' to see the full cofactor expansion or adjugate calculation.

Matrix Calculator FAQ

How do I multiply two matrices?
Enable two-matrix mode and enter both matrices. Matrix A (m×n) multiplied by Matrix B (n×p) gives a result of size m×p. The number of columns in A must equal the number of rows in B.

What is the determinant of a matrix?
A scalar value calculated from the matrix elements. For 2×2: det = ad − bc. A nonzero determinant means the matrix is invertible. A zero determinant means it is singular.

How do I find the inverse of a matrix?
The inverse A⁻¹ satisfies A × A⁻¹ = I (the identity matrix). It exists only when det(A) ≠ 0. This calculator shows the adjugate method step by step.

What is the transpose of a matrix?
The transpose flips rows and columns. If A has element a[i][j], then A^T has element a[j][i]. Useful in linear algebra and statistics.

What is row echelon form?
A matrix form reached via Gaussian elimination where each leading nonzero entry is to the right of the one above it. Reduced row echelon form goes further to fully reduce each pivot column.

What does it mean when the matrix is singular?
A singular matrix has determinant 0 and cannot be inverted. The tool warns you when this occurs.

What is the maximum matrix size?
6×6. This keeps calculations fast and the interface usable. Larger matrices can be solved programmatically.

Can I add matrices of different sizes?
No. Addition and subtraction require matrices to have the same number of rows and columns.

Can I paste data from a spreadsheet?
Yes. Copy cells from Excel or Google Sheets and paste into the grid — the calculator parses tab-separated values automatically.

Is any data sent to a server?
No. All calculations run entirely in your browser. Nothing is uploaded or stored.

Background

Perform a comprehensive range of matrix operations on an interactive grid. Set any matrix size from 2×2 to 6×6 using the row and column controls, enter values by clicking cells or pasting tab/comma-separated data, and choose from addition, subtraction, multiplication, scalar multiplication, transpose, determinant, inverse, row echelon form, and reduced row echelon form. Two-matrix mode enables operations that require two inputs such as multiplication and addition. Step-by-step solutions are provided for determinant (cofactor expansion) and inverse (adjugate method) operations — essential for linear algebra coursework. The tool checks dimension compatibility before multiplication and warns when a matrix is singular (non-invertible). Useful for students in linear algebra and engineering courses. All processing runs in your browser with no software installation required.

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