The amount of closed binary operations on A under these conditions are what? I have this problem and I would love some feedback on some of the answers that I have gave if they are incorrect. For some that I couldn't explain can someone explain to me how answers were achieved?.
Let:
$$A = \{a,b,c,d,x\}$$
Q: How many closed binary operations on $A$ have $x$ as the identity?
$5^{16}$, because $9$ operations with $x$ as the identity therefore $5^{25-9}$
Q: Of the $5^{16}$ closed binary operations on $A$ where $x$ is the identity, how many are commutative?