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