Let us take set A = {2, 3}

A × A × A = {2, 3} × {2, 3} × {2, 3}

   

Element

1 st element

{ 2 , 3} × { 2 , 3} × { 2 , 3}

(2, 2, 2)

2 nd element

{ 2 , 3} × { 2 , 3} × {2, 3 }

(2, 2, 3)

3 rd element

{ 2 , 3} × {2, 3 } × { 2 , 3}

(2, 3, 2)

4 th element

{ 2 , 3} × {2, 3 } × {2, 3 }

(2, 3, 3)

5 th element

{2, 3 } × { 2 , 3} × { 2 , 3}

(3, 2, 2)

6 th element

{2, 3 } × { 2 , 3} × {2, 3 }

(3, 2, 3)

7 th element

{2, 3 } × {2, 3 } × { 2 , 3}

(3, 3, 2)

8 th element

{2, 3 } × {2, 3 } × {2, 3 }

(3, 3, 3)

∴ A × A × A = {(2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 2, 2), (3, 2, 3), (3, 3, 2), (3, 3, 3)}

 

Note:

A × A × A = {(a,  b,  c) :  a,  b,  c ∈ A}.

Here (a,  b,  c) is called an  ordered triplet

  1. Chapter 2 Class 11 Relations and Functions
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.