A binary operation * on the set {0,1,2,3,4,5} is defined as: `a*b={a+b a+b-6"\ \ \ \ if\ "a+b<6"\ \ \ if"\ a+bgeq6` Show that zero is the identity for this operation and each element a of the set is invertible with 6a, being the inverse of a.

Explanation

To solve the problem, we need to show two things:

1. That 0 is the identity element for the binary operation defined.
2. That each element \( a \) of the set is invertible with \( 6 - a \) being the inverse of \( a \).

Let's break it down step by step.

### Step 1: Show that 0 is the identity element
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