How do you compute the number of reflexive relation? Given a set with $n$ elements
I know that there is $2^{n^2}$ relations, because there are $n$ rows and $n$ columns and it is either $1$ or $0$ in each case, but I don't know how to compute the number of reflexive relation. I am very dumb. Can someone help me go through the thought process?

A relation $R$ on $A$ is a subset of $AXA$. 
If $A$ is reflexive, each of the $n$ ordered pairs $(a,a)$ belonging to $A$ must be in $R$. 
So the remaining $n^2-n$ ordered pairs of the type $(a,b)$ where $a!=b$ may or may not be in R. 
So each ordered pair has now 2 choices, to be in $R$ or to not be in $R$. 
Hence number of pairs = 2($n^2-n$) 
