The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A and the remaining elements of A × A.
Given: Cartesian product A × A having 9 elements among which are found (–1, 0) and (0,1).
Number of elements in (A× B) = (Number of elements in set A) × (Number of elements in B)
⇒ n(A × A) = n(A) × n(A)
⇒ n(A × A) = 9 (given)
⇒ n(A) × n(A) = 9
⇒ n(A) = 3
By definition A × A = {(a, a): a Є A}.
Therefore, -1, 0 and 1 are the elements of set A.
Because, n(A) = 3 therefore, A = {-1, 0, 1}.
Hence the remaining elements of set (A × A) are:
(-1,-1), (-1,1), (0,0), (0, -1), (1,1), (1, -1) and (1, 0).