Application of Extended Euclidean Algorithm to find Multiplicative Inverse Modulo N

Given two integers 'a' and 'n'

Can we find an 'x' such that x * a is congruent to 1 MODULO n?

So, 'x' is actually the multiplicative inverse of 'a' modulo 'n' i.e.

x = (inverse a) MODULO n

Now, we can apply Extended Euclidean Algorithm to calculate: (inverse a) MODULO n

NOTE: We can find such an 'x' only when both 'a' and 'n' are co-prime to each other i.e. gcd(a, n) = 1