Key Formulas
2×2 Determinant: det(A) = ad − bc
Addition: (A+B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Addition: (A+B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Common Mistakes
- Adding matrices of different dimensions — addition and subtraction require identical dimensions on both matrices.
- Using entry-wise multiplication instead of row-column multiplication — these are different operations with different rules.
- Forgetting the determinant sign convention when expanding larger matrices — signs alternate (+,−,+,−) across the row or column used for expansion.
Frequently Asked Questions
What does a zero determinant mean?
It means the matrix is "singular" — it cannot be inverted, and the transformation it represents collapses space into a lower dimension (a line or point).
How do I find a 3×3 determinant?
Use cofactor expansion along any row or column: multiply each entry by the determinant of the 2×2 matrix remaining after removing that entry's row and column, alternating plus and minus signs as you go.
