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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