A has 4 elements.So, $A*A$ has 16 elements.
let us take a example. Let A ={a,b,c,d}
$A*A=\{aa,bb,cc,dd,ab,ac,ad,ba,bc,bd,ca,cb,cd,da,db,dc\}$
Here iam representing ordered pair (a,b) with ‘ab’
Ordered pairs aa,bb,cc,dd has no choice they have to be present in every reflexive relation.
But remaining 12 ordered pairs have 2 choices:Present or not present in a reflexive relation.
With each of these12 ordered pairs having 2 choices, we have $2^{12}$ relations each of which is reflexive.