---
title: "Matrix Calculator — 2×2 and 3×3 Add, Subtract, Multiply, Transpose, Determinant"
description: "Calculate 2×2 and 3×3 matrix operations: addition, subtraction, multiplication, transpose, and determinant. Covers row vs column vector conventions (US vs EU textbooks). For A-Level, IB, and university linear algebra."
url: "https://worldcalculators.org/calculators/matrix/"
canonical: "https://worldcalculators.org/calculators/matrix/"
---

# Matrix Calculator

Calculate 2×2 and 3×3 matrix operations: addition, subtraction, multiplication, transpose, and determinant. Covers row vs column vector conventions (US vs EU textbooks). For A-Level, IB, and university linear algebra.

## Quick answer

Matrix A

## Frequently Asked Questions

European mathematics textbooks (UK, Germany, France) traditionally write vectors as column vectors, which means transformations are applied as T×v (matrix times column vector on the right). In US computer science and machine learning contexts, row vectors are often used, meaning transformations are applied as v×T (row vector times matrix on the left). NumPy and most ML frameworks use row-vector convention by default (shape [n] is treated as a 1×n row vector). This causes confusion when switching between textbooks and code. Always check which convention your textbook or software uses.
Matrices are foundational across many fields: Computer graphics (3D rotation, scaling, and translation matrices power every video game and 3D animation). Machine learning (neural networks are essentially large matrix multiplications). Cryptography (Hill cipher uses matrix operations). Economics (input-output analysis, Leontief model). Quantum mechanics (state matrices / density matrices). Engineering (finite element analysis, structural calculations). Google's PageRank algorithm is a matrix operation. Every major country's engineering curriculum includes matrix algebra for these reasons.

Source: https://worldcalculators.org/calculators/matrix/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.