How are there are 16 relations on a two element set?

Question

Let $A=[{a_{1}, a_{2}}]$

I can only think of four those being [(${a_{1}, a_{2}}$), (${a_{2}, a_{1}}$), (${a_{1}, a_{1}}$), (${a_{2}, a_{2}}$)]

supposedly there 16 relations and All but three relations on a two element set are transitive.

if you have any hints on how to figure out the other relations please let me know. I will be working figuring it out too. Thank you.

Answer 1

Recall the definition:

$R$ is a relation on a set $A$ if and only if $R\subseteq A\times A$.

Now ask yourself, how many elements, and therefore how many subsets, does $A\times A$ have?

Answer 2

Hint: A relation on $A$ is a subset of $A\times A$. In general not an element as you seem to think.