Determine the total number of binary operations on the set `S={1,\ 2}` having 1 as the identity element.

Explanation

Let `e` be the identity element.

`a*e=a=e*a`

given `e=1`

`{(1, 1), (1, 2), (2,1), (2, 2)}`

For `(1, 1)=>1*1=1`

For `(1, 2)=>1*2-2`

For `(2, 1)=>2*1=2`

For `(2, 2)=>2*2=>1, 2`
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