Number of elements of A × B = Number of Elements of A × Number of elements of B

So, if set A has 3 elements, set B has 2 elements

Number of elements of A × B = 3 × 2 = 6

Let us check

If A = {1, 2, 3}, B = {3, 4}

A × B = {(1, 3), (1, 4),

(2, 3), (2, 4),

(3, 3), (3, 4)}

Number of elements of A × B = 6

## If A × A has 9 elements, then how many elements does set A have?

We know that

Number of elements of A × A = Number of Elements of A × Number of elements of A

Number of elements of A × A = (Number of elements of A)
^{
2
}

9 = (Number of elements of A)
^{
2
}

(Number of elements of A)
^{
2
}
= 9

Number of elements of A = √9 = 3