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Linear Algebra

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Commutative Property

LINALG-C1XEOV

What does it mean to say that an operation $*$ is commutative on a set $S$?

A

An operation $*$ on a set $S$ is commutative if for all $x,y,z$ in $S$, $(x*y)*z=x*(y*z)$

B

An operation $*$ on a set $S$ is commutative if for all $a,b$ in $S$, $a*b=b*a$

C

An operation $*$ on a set $S$ is commutative if there exist $x,y$ in $S$, such that $x*y=y*x$

D

Both Choice 'B' and Choice 'C' are correct.

E

None of the above are correct.