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On Z an operation * is defined by a * ...

On `Z` an operation * is defined by `a` * `b=a^2+b^2` for all `a ,\ b in Z` . The operation * on `Z` is

A

(a) commutative and associative

B

(b) associative but not commutative

C

(c) not associative

D

(d) not a binary

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The correct Answer is:
(c) not associative
For commutativity,
Let, `a,b in Z`
`a` * `b=a^2+b^2`
`=b^2+a^2`
`=b` *`a`
`therefore a`*`b=b`*`a`
. Thus, * is commutative on `Z`.

For associativity,
...
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