Linear Algebra › Section B · Matrix algebra › Topic B.2
The inverse of a matrix
To solve 5x = 15 you multiply both sides by 1/5. Some square matrices have a partner that undoes them in the same way, and finding that partner turns out to be ordinary row reduction in disguise.
In this topic
- Undoing a matrix
- Definition and uniqueness
- The 2 × 2 formula
- Solving a system with the inverse
- Worked example: a 2 × 2 system
- Rules for inverses
- Elementary matrices
- Why row reduction finds the inverse
- Worked example: a 3 × 3 inverse
- Common mistakes to avoid
- Key takeaways
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