Question

Using the extended euclidean algorithm, find the multiplicative inverse of $12$in $Z26$

Answer 1

According to the Extended Euclidean Algorithm

The multiplicative inverse of an integer $b$in $Zn$will exist only if $GCD(n,b)=1$

Here$n=26$ and$b=12$. Clearly$GCD(26,12)\ne 1$

Therefore multiplicative inverse of $12$does not exist in $Z26$