Linear Algebra › Section C · Determinants › Topic C.2
Properties of determinants
Cofactor expansion defines the determinant, but its properties are what make it useful. Knowing how row operations, transposes and products change a determinant lets you compute it quickly and prove that it decides invertibility.
In this topic
- Why properties matter
- How row operations change the determinant
- Why the rules hold
- Computing a determinant by row reduction
- Worked example: reduce, then multiply
- The invertibility test
- Transposes and column operations
- Products, inverses and scalar multiples
- Linear in one row at a time
- Worked example: properties without entries
- Common mistakes to avoid
- Key takeaways
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