A logic problem by Owais Shah

If $A$ and $B$ are two positive integers such that the ratio between the 5-digit integer $\overline{BBB00}$ and the 3-digit integer $\overline{AAA}$ is equal to the 3-digit integer $\overline{B00}$ .

Knowign that $A+A+A=B$ , find the value of the product of the two 3-digit integers, $\overline{ABA}\times \overline{BAB}$ .