Show that the binary operation * on Z defined by a * b = 3a + 7b … - Vidyadip

Question

Show that the binary operation * on Z defined by a * b = 3a + 7b is not commutative.

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Answer

The binary operator * defined on Z and is given by a * b = 3a + 7b
Commutativity: Let $\text{a, b}\in\text{Z},$ Then,
a * b = 1a + 7b and
b * a = 3b + 7a
$\therefore\ \text{a}\ ^*\ \text{b}\neq\text{b}\ ^*\ \text{a}$
Hence, '*' is not commutative on Z.

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