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).


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