This question has to do with operations and exploring their characteristics. I have just learned how to extract info from an operations table (what is the identity, inverse, etc.), but this question is presented in an unfamiliar way and I am not sure how to find the answers to the two questions that are given.
$$ a*b = 2a + 3b $$ I am being asked to "find $3*4$" and whether or not the operation $*$ is commutative. Any help would be greatly appreciated!
On
I suspect you may be confused by the notation $a*b$, which in computing would mean the product, but in this case is just an arbitrary operation, defined by the formula $2a+3b$ . Putting it in a table is hard if it is meant to be defined for all reals: that makes the table so big! Once you understand the definition you should have no trouble following Sammy Black's advice.
In order to check whether the operation $*$ is commutative, you need to determine whether $$ a * b = b * a $$ for all $a$ and all $b$ in the real numbers. In other words, you need to figure out whether $$ 2a + 3b = 2b + 3a $$ for all real $a$, $b$. This could go one of two ways.
If it's TRUE, then you should be able to show that the left hand side is the same as the right hand side just using algebra.
If it's FALSE, then you just need a counterexample. In other words, you just have to find some real number $a$ and some other (possibly the same?) real number $b$ such that $$ 2a + 3b \ne 2b + 3a. $$