With  A =-((ℏ^2)/(2 m r^2)) (∂/(∂r))((r^2) (∂/(∂r))) , (Subscript[p, r])= -i ℏ (∂/(∂r))    , find that [A, (Subscript[p, r])] = -((ℏ^2)/(2 m r^2)) (Subscript[p, r])

ClearAll[hbar, A, pr, rn, display, a1]

display = {hbar -> ℏ} ;
a1[f_] := (r^2 D[f[r], {r}]) /. r-> # & ;
A[f_] := -((hbar^2/2/m/t^2) D[ a1[f] [t],{t}] )/. t-> # &;

pr[f_] := -I hbar D[f[s], {s}] /. s-> # & ;

rn[n_] := #^n & ;
pr[ rn[n] ][r] /. display
A[rn[n] ][r]    /. display
A[pr[rn[n]] ][r]  /. display
pr[A[rn[n]] ][r]  /. display

((A[pr[rn[n]] ][r] -  pr[A[rn[n]] ][r])  // Simplify) /. display
((A[pr[f] ][r] -  pr[A[f]][r])  / (-I hbar)// Simplify ) /. display