DETERMINANT OF A 2x2 MATRIX

DETERMINANT OF A 2x2 MATRIX

What is it?

ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.

In simple words

• ad-bc.
• [[1,2],[3,4]] -> -2
• Singular if det=0
• State the rule, show the working, and check the answer.

Important terms

DETERMINANT OF A 2x2 MATRIX: ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.

2x2: ad-bc.

What you should learn

• State the rule or meaning of determinant of a 2x2 matrix in easy words.
• Apply determinant of a 2x2 matrix in a clear step-by-step solution.
• Check the conditions, working, and final answer for accuracy.

Examples

• [[1,2],[3,4]] -> -2
• Singular if det=0
• det A^T = det A

MAIN IDEA

ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.

EXAM USE

Write the rule first: ad-bc. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Full school-level explanation

ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.

Understand the idea, then apply it:

WHAT — DETERMINANT OF A 2x2 MATRIX

ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.

WHY — Why it matters

This rule is a separate learning unit inside determinants 2x2 and 3x3. It can be defined, applied, and checked in its own FBISE question.

HOW — How to answer

Write the rule first: ad-bc. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

MAIN IDEA

ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.

Remember

• ad minus bc

Examples

• [[1,2],[3,4]] -> -2
• Singular if det=0
• det A^T = det A

EXAM USE

Write the rule first: ad-bc. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Remember

• focused answer
• accurate support

Examples

• State the central idea
• Use one accurate detail
• Check the final response

How to answer a determinant of a 2x2 matrix question

How it works

• 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.

Remember

• ad minus bc
• 2x2: ad-bc
• 3x3: cofactor expansion
• chessboard signs
• ad minus bc
• focused answer
• accurate support
• ad minus bc

Deeper understanding

Go beyond memorising DETERMINANT OF A 2x2 MATRIX. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

What to Know

Example or Evidence

How to Answer

Exam focus

Quick revision

• ad minus bc
• 2x2: ad-bc
• 3x3: cofactor expansion
• chessboard signs
• DETERMINANT OF A 2x2 MATRIX: ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.
• 2x2: ad-bc.

The sign is (-1)^i+j, not 'always plus'. Chessboard of + and -.

For long answers on DETERMINANT OF A 2x2 MATRIX: define clearly → explain the main parts → give one example → state one exam caution.