Given $a \ast b = \large\frac {ab} {4}$

Let e be the identity element of the * operation

then from definition of identity element a*e=e*a=a

from definition of * operation $a*e= \large\frac {ae} {4}$ =>$a= \large\frac {ae} {4}$ =.> e=4

Also$ e*a= \large\frac {ea} {4}$ =>$ a=\large\frac {ea} {4}$ => e=4

e =4 is the identity element,

solution - the given operation *given by $a \ast b = \large\frac {ab} {4}$ has a n identity element