Mathematics Asked by needHelp on November 7, 2020
Might be duplicate I don’t know but Properties of a binary operator; trouble understanding question.
begin{equation*}
begin{array}{c}
star : mathbb{Z} times mathbb{Z} to mathbb{Z}\
x star y = x + 3y
end{array}
end{equation*}
(d.) Can you find two integers a and b that commute for $star$? Explain.
Two integers $a$ and $b$ commute under (or for) $star$ if $astar b=bstar a$.
So we are looking for integers $a,b$ such that $$ a+3b = b+3a. $$
Correct answer by Christoph on November 7, 2020
Any operation $star$ commutes if $a star b = b star a$. An example of an operation that does not commute would be a matrix multiplication since if $A$ and $B$ are matrices, it is possible that $A cdot B neq B cdot A$, thus the $cdot$ operation is not commutative.
Answered by user822251 on November 7, 2020
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