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A binary operation * on the set \( \{0,1,2,3,4,5\} \) is defined as
\[
a * b=\left\{\begin{array}{ll}
a+b ; & \text { if } a+b6 \\
a+b-6 ; & \text { if } a+b \geq 6
\end{array}\right.
\]
\( \mathrm{P} \)
W
Show that 0 is the identity for this operation and each element \( a \) has an inverse \( (6-a) \).
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