What is an identity matrix?

It's a square matrix with 1 on every diagonal position (top-left to bottom-right) and 0 everywhere else. Multiplying any matrix by the identity matrix of the right size leaves it unchanged, the same way multiplying a number by 1 leaves it unchanged.

What size matrices does this support?

Any whole number size N from 1 to 20, producing an N by N matrix.

Why would I need an identity matrix?

It's commonly used as a starting point for computing a matrix inverse (via Gauss-Jordan elimination), as a neutral element in matrix multiplication, and in linear algebra coursework and proofs.

Identity Matrix Generator - Create an NxN Identity Matrix Online

Overview

Introduction

The identity matrix is one of the most fundamental objects in linear algebra, the matrix equivalent of the number 1.

This tool builds one instantly for any size you need, formatted for use with the site's other matrix tools.

What Is Generate an Identity Matrix?

A square matrix of size N by N where every diagonal entry is 1 and every off-diagonal entry is 0.

For example, the 3x3 identity matrix has 1s at positions (1,1), (2,2), and (3,3), and 0 everywhere else.

How Generate an Identity Matrix Works

The input size N is validated as a whole number from 1 to 20, then an N by N grid is built where each cell is set to 1 if its row index equals its column index, and 0 otherwise.

The result is formatted in the site's standard matrix notation, rows separated by newlines and values within a row separated by commas.

When To Use Generate an Identity Matrix

Use it whenever you need a starting identity matrix for a manual calculation, a homework problem, or as test input for the Matrix Inverse or Matrix Multiplication calculators.

It's also a quick way to confirm what an identity matrix of a given size looks like.

Often used alongside Matrix Inverse Calculator, Generate Random Matrices and Transpose a Matrix.

Features

Advantages

Instant, exact output with no chance of a manual transcription error.
Works for any size from 1x1 up to 20x20.

Limitations

Only produces square identity matrices, there's no option to generate a rectangular variant.

Examples

3x3 identity matrix

Input

Output

1,0,0
0,1,0
0,0,1

Diagonal positions (1,1), (2,2), and (3,3) are 1; every other position is 0.

Best Practices & Notes

Best Practices

Match the size N to the matrix you're working with, an identity matrix only combines correctly with matrices of the same dimensions.

Developer Notes

The matrix is built with Array.from() using the row and column indices directly: `row === col ? 1 : 0`, so there's no branching cost beyond a single comparison per cell.

Generate an Identity Matrix Use Cases

Setting up the augmented matrix for Gauss-Jordan matrix inversion by hand
Verifying that a computed inverse is correct (a matrix times its inverse should equal the identity matrix)
Linear algebra coursework and reference

Common Mistakes

Assuming an identity matrix can be non-square, it's always N by N for a single size N.

Tips

Feed this tool's output straight into Matrix Multiplication Calculator to confirm A times I equals A for any matrix A.

Generate an Identity Matrix