Please help ASAP. please ensure to use step by step explanation. thanks.

I'll do the first two parts to get you started.

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Part (i)

We can show that the operation is not commutative by picking two random and different real numbers for a,b. In other words, I'm using a counter-example.

Let's say we go for a = 1 and b = 2

Now let's swap the values. We'll try a = 2 and b = 1

We can see that and are not the same value. In general, Therefore, the operation is not commutative.

The only time is true is when , since,

It's when is where the operation becomes noncommutative.

Another way to arrive at the condition is to solve the original equation for either 'a' or b.

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Part (ii)

Using the previous part as inspiration, we'll do a counter-example to show that the operation is not associative. Pick 3 random values for a,b,c. Here are the values I'll pick.

Then,

Next, we can say:

Let's compare the two outputs:

They don't match up, so when (a,b,c) = (1,2,3).

In general, the operation is not associative in R.

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step-by-step explanation:

i took the test: )