a,b are elements of the group G
I have no idea how to even start - I was thinking of defining a,b as two square matrices and using the non-commutative property of matrix multiplication but I'm not sure if that's the way to go...
a,b are elements of the group G
I have no idea how to even start - I was thinking of defining a,b as two square matrices and using the non-commutative property of matrix multiplication but I'm not sure if that's the way to go...
Since you want this to be in a group, take the group of permutations of $\{1,2,3\}$ and take the counterexample $a$ and $b$ to be two distinct transpositions, say $(1,2)$ and $(2,3)$.
Consider the multiplicative subgroup of the quaternions consisting of $\pm 1$, $\pm i$, $\pm j$, and $\pm k$. Let $a=i$ and $b=j$. We have $ij^2=-i$ and $j^2i=-i$ but $ij\ne ji$.