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Let * be a binary operation on N, the se...

Let * be a binary operation on N, the set of natural numbers, defined by `a`*`b=` `a^b` for all `a , b in Ndot` Is `'*'` associative or commutative on `N ?`

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Here, `a`*`b=a^b`
for all `a,b in N`.
Now, `a`*`b=a^b` and `b`*`a=b^a`
`implies a`*`b=b`*`a`
Therefore, it is not commutative.
Let `a,b,c in N`
`(a`*`b)`*`c=(a^b)`*`c`
`(a`*`b)`*`c=(a^b)^c`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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