MathematicsChapter 2: Matrices and Determinants
Find A^{-1}
If det=0, stop: no inverse.
Learning objectives
- State the rule or meaning of find a-1 in easy words.
- Apply find a-1 in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A-1 = I on one row if time.
Formula
det=0
Where / symbols
- FIND A^{-1}
- If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A^{-1} = I on one row if time.
- FIND A^{-1}
- If det=0, stop: no inverse.
Relationship
- invertible <-> det != 0 (square)
- rank = number of pivots
Overview
Understand the idea, then apply it:
Main Idea
If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A-1 = I on one row if time.
Examples 2x2 adjugate / det · [A|I] -> [I|A^{-1}] · No inverse if a row becomes 0 | junk
Exam Use
Write the rule first: If det=0, stop: no inverse. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — FIND A^{-1}
If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A-1 = I on one row if time.
WHY — Why it matters
This rule is a separate learning unit inside inverse and rank (row operations). It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: If det=0, stop: no inverse. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a find a^{-1} question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
If det=0 there is no inverse. Do not divide by zero.
Key points
- det first
- invertible <-> det != 0 (square)
- rank = number of pivots
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Find A^{-1}
Sticky Notes · Quick Revision
Core Idea
- If det=0, stop: no inverse.
What to Know
- If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A-1 = I on one row if time.
Example or Evidence
- 2x2 adjugate / det
- [A|I] -> [I|A-1]
- No inverse if a row becomes 0 | junk
How to Answer
- Write the rule first: If det=0, stop: no inverse. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- If det=0 there is no inverse. Do not divide by zero.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- If det=0, stop: no inverse.
- 2x2 adjugate / det
- [A|I] -> [I|A-1]
- State the rule, show the working, and check the answer.
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