I don't understand the meaning of commute and i can't find any info about it

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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