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

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

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

Then we can define the given binary operation.

For example, `1 * 1=(1 cdot 1) bmod 5=2`

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

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

`4 * 4=(4 cdot 4) mod 5=1`

Similarly, we can define the given binary operation on each order pair of `A`.

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