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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.
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Product Law
What is it?
You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
In simple words
- You cannot write (AB)^T = A^T B^T in general.
- reverse the product
- rows <-> columns
- (AB)T = BT AT
Important terms
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.
What you should learn
- Define and explain product law.
- Apply product law to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Examples
- reverse the product
- rows <-> columns
- (AB)T = BT AT
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.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 10
Full school-level explanation
You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
Learn the idea, then use it:
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.
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.
Remember
- reverse the product
- rows <-> columns
- (AB)T = BT AT
Examples
- reverse the product
- rows <-> columns
- (AB)T = BT AT
- 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.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- reverse the product
- rows <-> columns
- (AB)T = BT AT
- keep the ideas separate
- reverse the product
- rows <-> columns
- (AB)T = BT AT
- correct term
Deeper understanding
Go beyond memorising Product Law. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- reverse the product
- rows <-> columns
- (AB)T = BT AT
- keep the ideas separate
- 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.
- 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.
Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Product Law: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- reverse the product
- rows <-> columns
- (AB)T = BT AT
- keep the ideas separate
Important formulas
- reverse the product
- rows <-> columns
- (AB)T = BT AT
Common exam traps
- Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
reverse the product
rows <-> columns
(AB)T = BT AT
keep the ideas separate
You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
(AB)T = BT AT
- Definition
- You cannot write (AB)^T = A^T B^T in general. Reverse the order: B^T A^T. Same warning as AB != BA.
- Formula
- (AB)T = BT AT
- Example
- reverse the product
- Critical warning
- Do not merge product law with a neighbouring idea that uses a different definition, rule, or method.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Ready to test yourself?
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Exam Practice
Define
Q1. Define Product Law.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Product Law and say why it fits.
Mistake
Q4. State one common mistake students make about Product Law.
Exam note
Q5. Write a short exam note on Product Law: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.