Find the additive inverse of $[33]_{60}$ in $(\mathbb{Z} / 60,+)$

Question

Find the additive inverse of $[33]_{60}$ in $(\mathbb{Z} / 60,+)$.

In my textbook there is a theorem I can use to find the multiplicative inverse. But I could not find any result which I can use to find the additive inverse. It's a multiple choice and I have six choices I can choose from, but that will be just guesswork.

Which mathematical results and definitions should I use?

Answer 1

HINT:
You can obtain the inverse of $x$ by subtracting it from the modulus as:
$$x+(n-x) = n = 0$$

Answer 2

Here's a couple of theorems you can use ( however advanced):

The inverse ( additive or multiplicative) modulo a composite number $n$ is also a valid inverse modulo the prime powers dividing $n$

This can be coupled with the theorem below:

Chinese remainder theorem/generalization: There exists a remainder modulo the lcm of moduli, for any set of remainders modulo the moduli . This can be found by turning them into linear form, and setting them equal to solve.

Note : the first theorem can be generalized to quadratic residues, and coprime residues, etc.

EDIT :Here's another one any time a multiplicative inverse $x$ exists, Letting $y$ be the additive inverse: $$xy\equiv-1$$ The real uselessness is a multiplicative inverse need not always exist, while the additive inverse always exists in the more general settings.