Define a binary operation * on the set `A={0,1,2,3,4,5}` given by `a*b=a b` (mod 6). Show that 1 is the identity for *. 1 and 5 are the only invertible elements with `1^(-1)=1` and `5^(-1)=5`

Explanation

Given the set `X=0,1,2,3,4,5` where the binary operation ∗ is defined by

`⇒a∗b={a+b` if `a+b<6a+b−6 ` if `a+b≥6}`

An element `e in N` is an identity element for operation
∗ if `a∗e=e∗a` for all `a in N`

To check if zero is the identity, we see that
`a∗0=a+0=a` for `a in x` and also
`0∗a=0+a a in x`

Given `a in X` `a+0<6` and also `0+a<6`
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