If $\ast$ is a binary operation on the set $(\{0, 1, 2, 3, 4, 5\})$ defined as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] then draw the composition table for the operation and find the identity element and inverse of $4$ if exists.

Question

$\begin{array}{1 1} \text{0 is identity and inverse of 4 is 2}\\ \text{identity and inverse do not exist} \\\text{0 is identity and inverse does not exist} \\ \text{1 is identity and inverse of 4 is 4} \end{array} $