On the set of integers $\mathbb{Z}$ define a binary operation $*$ by $a * b = a + b - 3$ for all $a,b\in\mathbb{Z}$. (i) State whether $*$ is associative. (ii) Find the identity element of $*$ in $\mathbb{Z}$.

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Accepted Answer

Associative; identity element = 3

Neco 2021 Further Mathematics Question 20

On the set of integers \(\mathbb{Z}\) define a binary operation \(\) by \(a b = a + b - 3\) for all \(a,b\in\mathbb{Z}\). (i) State whether \(\) is associative. (ii) Find the identity element of \(\) in \(\mathbb{Z}\).

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Neco 2021 Further Mathematics Question 20

On the set of integers \(\mathbb{Z}\) define a binary operation \(*\) by \(a * b = a + b - 3\) for all \(a,b\in\mathbb{Z}\). (i) State whether \(*\) is associative. (ii) Find the identity element of \(*\) in \(\mathbb{Z}\).

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On the set of integers \(\mathbb{Z}\) define a binary operation \(\) by \(a b = a + b - 3\) for all \(a,b\in\mathbb{Z}\). (i) State whether \(\) is associative. (ii) Find the identity element of \(\) in \(\mathbb{Z}\).