Common Mistakes

Frequent Errors

1. Building A with basis images in wrong columns (4.13.A.2). 2. Rotation matrix sign errors (4.13.A.3). 3. Using det instead of |det| for area dilation magnitude (4.13.A.4). 4. Reversing composition order AB vs BA (4.13.B.2). 5. Assuming transformations commute. 6. Finding inverse when det=0 (4.13.C.2, 4.11.B.3). 7. Not connecting graph/diagram to matrix entries (2.A). 8. Vague descriptions without precision (3.A).

Why These Happen

Students memorize rotation formula without linking to basis images.

How to Fix Them

• Columns of A are images of (1,0) and (0,1).
• Track order: first transformation applied corresponds to matrix placement in product.
• Check det before inverting.

Avoidance Scripts

• Columns come from basis images.
• Order matters in composition.
• |det| for area scaling magnitude.

Quick Self-Check

• Are columns correct?
• Is rotation matrix signed correctly?
• Did I multiply in the right order?