A is correct.
Here P is non singular of order 4 i.e $|P| \neq 0$. So rank of P is 4
Assuming A and B are multiplication compatible. (which here they are)
so rank(AD) $\leq$ min(2,4)
rank(AD) $\leq$ 2.
But the column rank of a matrix is invariant under pre multiplication by a non singular matrix. Similarly the row rank of a matrix is invariant under post multiplication by a non singular matrix.
So it will be 2.
Ref: www.biostat.jhsph.edu › ~iruczins › teaching › cr.intro.pdf