Common Mistakes
Frequent Errors
1. Stating m x n when matrix is n x m (rows first) (4.10.A.1). 2. Attempting AB when columns of A != rows of B (4.10.A.2). 3. Multiplying corresponding entries instead of row-column dots (4.10.A.2). 4. Using wrong row or column for entry (i,j) (4.10.A.2). 5. Product dimension stated as m x n instead of n x m from (n x p)(p x m) (4.10.A.2). 6. Assuming matrix multiplication is commutative. 7. Dot product arithmetic slips (4.8.B.3 link). 8. Misreading which matrix is first in AB (4.10.A.2).
Why These Happen
Students treat matrices like scalars or skip dimension checks.
How to Fix Them
- Always write dimensions before multiplying.
- One entry at a time with explicit row and column.
- Verify product size with outer dimensions.
Avoidance Scripts
- "Inner match, outer size."
- "Row from left, column from right."
- "Dot, don't multiply straight across."
Quick Self-Check
- Did I check compatibility?
- Did I use row i dot column j?
- Is the product dimension correct?