Let, f:Z-->Z be a function defined by:- f(s)= as + b , for certain integers a and b. Then, for what values of a and b, f○f will be an identity map?
I read the Wikipedia article on identity functions (assuming identity map and identity function are synonymous) and believe I can help.
$\displaystyle f(x)$ is an identity function if $\displaystyle f(x) = x$. Therefore, $\displaystyle f(f(s))$ is an identity function if $\displaystyle f(f(s)) = f(s)$.
$\displaystyle f(f(s)) = af(s) + b = a(as + b) + b = a^2s + ab + b
$
Solve the equation $\displaystyle a^2s + ab + b = as + b$ for $\displaystyle a$ and $\displaystyle b$.