Show that $*: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ defined by $a * b = a + 2b$ is not commutative.
(N/A) To check if the operation $*$ is commutative,we need to verify if $a * b = b * a$ for all $a, b \in \mathbb{R}$.
Given $a * b = a + 2b$.
Let us take two real numbers,$a = 3$ and $b = 4$.
Then,$a * b = 3 * 4 = 3 + 2(4) = 3 + 8 = 11$.
Now,calculate $b * a = 4 * 3 = 4 + 2(3) = 4 + 6 = 10$.
Since $a * b \neq b * a$ (because $11 \neq 10$),the operation $*$ is not commutative.
Given $a * b = a + 2b$.
Let us take two real numbers,$a = 3$ and $b = 4$.
Then,$a * b = 3 * 4 = 3 + 2(4) = 3 + 8 = 11$.
Now,calculate $b * a = 4 * 3 = 4 + 2(3) = 4 + 6 = 10$.
Since $a * b \neq b * a$ (because $11 \neq 10$),the operation $*$ is not commutative.
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