I was doing example 1 Page 94 from Joseph A Gallian ,
In question it was given $\alpha = (231)$ and $\beta = (132) $ and then on next page there is $$ \alpha\beta = (21) $$ .
So if we think permutation as composition of functions that is $\alpha[\beta(x)]$ and take $x=1,2,3$ then thr answer seems right .
But in book Topics in algebra by I.N. Herstein permutations are operated from left to right so answer should be $(23)$ .
So which answer is right as both books are one of best books for algebra . I am very confused .
Both conventions, left-to-right and right-to-left, are in common use. Either one is okay as long as it is used consistenly. Neither is "right" or "wrong". The convention affects the result of computations but it doesn't affect any of the general theorems. When reading a book or article, using the convention of that book or article will usually make things easier to follow.