Step by step
The question
Question: find A × A, when A is {1, 2, 3} and B is {7, 8}.
A = {1, 2, 3}, B = {7, 8}
A × A means: every pair with the first number from A and the second from A.
A pair is written in round brackets.
A × A = every pair (first from A, second from A)
1 Make the table
Across the top: the elements of A.
Down the side: the elements of A.
Each cell is a pair: its row first, its column second.
1 with 1 is (1, 1).
2 List the pairs
We write the pairs row by row, inside curly brackets: (1, 1), (1, 2) and so on.
A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
3 Check
Let's check the count: 9 pairs, and 3 times 3 is 9.
No pair twice.
So it is right!
9 pairs = n(A) × n(A) = 3 × 3
Let's look back.
First: make the table.
Then: list the pairs.
Last: check.
Answer
A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}