Question

If $A$ has $2$ elements and $B$ has $2$ elements, then the number of elements in $B\times A$ is :

Answer 1

Cartesian product of two sets contains ordered pair of elements of both the sets.
Suppose $A=\{x,y\}$ then $B=\{x,y\}$ as both sets are equal.
Then $A\times B=\left\{\right(x,x),(x,y),(y,x),(y,y\left)\right\}$
And $B\times A=\left\{\right(x,x),(x,y),(y,x),(y,y\left)\right\}$

Thus the number of elements in $B\times A$ is $4$