equivalence relations - fine the inverse of $[2]$ and $[23]$ in$ mathbb{Z}_{41}$

I know the inverse of [23] is

[23] * [25] = 575

575 congruent to 1 mod 41

[25] is the inverse

I have started the other one but I am doing something wrong I got

[2] * [41] = [82] = [0]

82 congruent to 0 mod 41

I thought 41 would be the inverse but it is not.