Common Mistakes
Frequent Errors
1. Using ad+bc instead of ad-bc for det(A) (4.11.B.1). 2. Finding an inverse when det(A)=0 (4.11.B.3). 3. Not verifying AA^-1=I (4.11.A.3). 4. Forgetting identity matrix structure (4.11.A.1). 5. Treating AI as undefined (4.11.A.2). 6. Using signed det for area without |det| when area is requested (4.11.B.2). 7. Arithmetic slips in 2x2 inverse formula (4.11.A.4). 8. Confusing parallel vectors with perpendicular when det=0 (4.11.B.2).
Why These Happen
Students jump to inverse formulas before checking determinant.
How to Fix Them
- Always compute det(A) first.
- Verify inverse by multiplication.
- Use |det| for area questions.
Avoidance Scripts
- Det first, inverse second.
- Zero det means no inverse.
- Multiply back to check I.
Quick Self-Check
- Did I use ad-bc?
- Is det(A) nonzero before inverting?
- Did I verify AA^-1=I?