# matrix inverse

(1.8 hours to learn)

## Summary

The inverse of a matrix A is a matrix which, when multiplied by A, gives the identity matrix. When it exists, it can be used to solve systems of linear equations.

## Context

This concept has the prerequisites:

- linear systems as matrices (The matrix inverse is defined in terms of systems of linear equations.)
- matrix multiplication (The inverse of a product is the product of the inverses, reversed.)

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

→ Khan Academy: Linear Algebra

Other notes:

- Watch the "Functions and linear transformations" lecture sequence if you're not used to thinking of matrices as linear transformations.

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 2.5, up to "Calculating A^-1 by Gauss-Jordan elimination", pages 81-83

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 1.4.1, "Algebra of linear functions," from pages 34-36

## See also

- The inverse of a matrix can be interpreted in terms of systems of linear equations .