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Matrix Calculator (2×2 / 3×3)

DeveloperMath

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INPUT

Auto Process

OUTPUT

Client Side

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Guide

Matrix Calculator (2×2 / 3×3)

The Matrix Calculator lets you add, subtract, multiply, transpose, and find the determinant or inverse of 2×2 and 3×3 matrices using a clean visual grid. Enter your numbers directly into the matrix cells and get instant, exact results — no rounding errors, no setup, and no math software required.

Unlike a chat box, this tool renders a real grid and computes with exact rational arithmetic, so a fraction like 1/3 stays 1/3 instead of becoming a long, lossy decimal. That makes it reliable for homework, engineering checks, and quick verification of linear-algebra work.

How to Use

Choose the matrix size: 2×2 or 3×3.
Select the operation you want — add, subtract, multiply, transpose, determinant, or inverse.
Type the values into the grid cells. You can enter whole numbers, decimals (e.g. 2.5), or fractions (e.g. 1/3).
For binary operations (add, subtract, multiply) fill in both Matrix A and Matrix B.
Read the result instantly, and switch the output between exact fractions and decimals.
For determinant and inverse, expand the step-by-step working to see exactly how the answer was derived.

Features

Six operations – Addition, subtraction, multiplication, transpose, determinant, and inverse.
2×2 and 3×3 support – Toggle the grid size with a single click; your entered values are preserved.
Exact fraction arithmetic – Uses rational (BigInt) math so results are precise, not approximate.
Fraction or decimal output – Switch between exact fractions and rounded decimals instantly.
Step-by-step working – See the cofactor expansion for determinants and the adjugate method for inverses.
Fully client-side – Everything runs in your browser; your data never leaves your device.

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 FAQ

What does the determinant of a matrix tell you?

The determinant is a single number that summarizes key properties of a square matrix. Geometrically it represents how much the matrix scales area (2×2) or volume (3×3). A determinant of zero means the matrix is singular and collapses space onto a lower dimension, which is why such matrices cannot be inverted.
When does a matrix have no inverse?

A square matrix is invertible only when its determinant is non-zero. If the determinant equals zero, the rows or columns are linearly dependent, the transformation is not reversible, and no inverse exists. These are called singular matrices.
Why is matrix multiplication not commutative?

For matrices A and B, the product A×B is generally not equal to B×A because each entry of the result is a dot product of a row from the first matrix with a column from the second. Swapping the order changes which rows meet which columns, so the products usually differ in both values and even dimensions.
What is the transpose of a matrix used for?

The transpose flips a matrix across its main diagonal, turning rows into columns. It is fundamental in many areas such as computing dot products, defining symmetric matrices, least-squares regression, and converting between row and column vector representations.