MathematicsChapter 3: Matrices and Determinants
Product Law
You cannot write (AB)^T = A^T B^T in general.
Learning objectives
- Define and explain product law.
- Apply product law to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Statement
You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
Formula
T = AT BT in general. Reverse the order
Where / symbols
- Product Law
- You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
Relationship
- (AB)T = BT AT
Overview
Learn the idea, then use it:
Core Understanding
You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
Examples reverse the product · rows <-> columns · (AB)^T = B^T A^T · PRODUCT LAW: You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — PRODUCT LAW
You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
Key points
- reverse the product
- rows <-> columns
- (AB)T = BT AT
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Product Law
Sticky Notes · Quick Revision
Core Idea
- You cannot write (AB)^T = A^T B^T in general.
Key Points
- reverse the product
- rows <-> columns
- (AB)T = BT AT
Simple Check
- Explain product law in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- You cannot write (AB)^T = A^T B^T in general.
- reverse the product
- rows <-> columns
- (AB)T = BT AT
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