modular arithmetic - Multiplicative inverse of 97 modulo 386?

A little help would be a lifesaver :)

I already used the Euclidean algorithm to find the GCD of $386$ and $97$, which is $1$. However, I'm stuck on this question posed by my professor: "Then use your computation to explain the statement: $241$ is the multiplicative inverse of $97$ $\mathrm{modulo}$ $386$."

I've been stuck on the topic of multiplicative inverses for days so any help would be greatly appreciated. Thank you so much!