A binary operation * on the set (0,1,2,3,4,5} is defined as : $f(x) = \left\{ \begin{array}{l l}a+b, & \quad if { a+b < 6} \\ a+b-6, & \quad if { a+b \geq 6} \end{array} \right.$ Show that zero is the identity for this operation and each element 'a' of the set is invertible with 6-a, being the inverse of 'a'.

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