If c*a = b*c, then a = b ?

If c*a = b*c, then a = b ?

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en.wikipedia.org/wiki/Matrix_similarity
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Yes because you can divide the equation by c.

Fucktard.

u can divide only if u know that G is commutive, otherwise not at all

Yeah, but if it is a non abelian group?

Not if c is the multiplicative identity :^)

Also, so long as c =/=0

with multiplication notion there is no 0, basic group propertys u fucker

>basic group propertys
>no 0

you retarded, senpai?

with "*" 1 is used as identity, with "+" 0, G is said to be group not ring

OP indicated that the group operation is multiplication. Hence [math]0[/math] can't be part of the group because there's no inverse element [math]0^{-1}[/math] such that [math]0*0^{-1}=1[/math].

It's really not specified what set we're dealing with, so I guess one could invent an inverse to 0 if they really wanted to. That's a bit beyond me though.

fuck no, a=c^{-1}bc

No unless your group is Abelian.

Then b=c*a*c^-1, and the rest depends on whether a and c commute.

>a=c^{-1}bc
This.
You have equality iff c*a = a*c. Also iff c*b = b*c.
Also, for the Rubik's Cube group, it should be obvious that [math]c^{-1}bc[/math] is often different from [math]b[/math]. You should be familiar with what transforming [math]b \to c^{-1}bc[/math] does, as it is important for solving the thing.

If G is abelian, then yes. If G is nonabelian, then this doesn't hold for arbitrary a,b,c.

For a nonabelian example, you can find a,b,c in S_3 quite quickly that satisfy ca = bc but a is not equal to b.

Extra little note: if a group G has the property that ca = bc implies a=b for any a,b,c in G, then G is abelian. That's a nice little exercise that's easy if you can work through the logic.

Even if you were working in a ring, you have problems with c=0 and zero divisors.

It's true if a,b, and c are the only elements in the group.

thanks dude. I was looking for a counterexample.

>fucktard

If and only if * is commutative, simplifiable and c is not an absorbing element of *.

Any other reply is brainlet-tier.

I think quaternions are a counterexample.

>the only group I know are the reals

Fucktard.

>high-schooler

leave Veeky Forums forever

...

>If c*a = b*c, then a = b ?

Only in an abelian groups, but for matrices a and b are similar, which is an equivalence relation too.

en.wikipedia.org/wiki/Matrix_similarity

*provided c is regular ofc