Let $A=\{a,b,c,d\}.$ Consider th following table for the binary operation $*$: A x A $A$ :

$\backslash$table$[[**,$a$,$b$,$c$,$d$],[$a$,$d$,$c$,$b$,$d$],[$b$,$c$,$d$,$a$,$b$],[$c$,$b$,$b$,$d$,$c$],[$d$,$d$,$b$,$c$,$c$]]$

Which of the following is true regarding an identity element for operation $*?$

Select one:

a$.$ d is the identity element.

b$.b$ is the identity element.

c$.$ c is the identity element.

d$.*$ does not have an