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

Explanation

Here, `A = {1,2,3,4}.`

And, `a**b = ab mod 5.`
So, if we take any two elements from `A`,

Then we can define the given binary operation.

For example,
`1**1 = (1*1) mod 5 = 2`

`2**2 = (2*2) mod 5 = 4`

`2**3 = (2*3) mod 5 = 1`

...