If $|B\times A| = 15$ ,evaluate: $|A\cap B|$

Question

If $|B\times A| = 15$ and $|A\times B \backslash B \times B| = 12$.

Evaluate: $|A\cap B|$

I tried for myself and got to the conclusion that $|A\times B \cap B \times B| = 3 $

I couldn't get by myself to the point where I know how to evaluate $|A\cap B|$

Some help?:) Thanks

Answer 1

Hint: $(A\times B)\cap (B\times B)=(A\cap B)\times B$

Answer 2

$|B \times A| = nm = 15$

$|(A \times B) \setminus (B \times B)| = | (A \setminus B) \times B| = (|A| - |A \cap B|) \times |B| = (m-x)n = 12$

$mn-(m-x)n=3, nx=3$
$(m-x)3/x=12$
$m/x=5$

easy to guess that $m=5, n=3, x=1$

$|A \cap B| = 1$