1. Extended Euclidean Algorithm for `11` and `12`

Solution:
`y-=z^(-1)\ ("mod "n)-=11^(-1)\ ("mod "12)-=11\ ("mod "12)`

Extended Euclidean Algorithm

i	Quotient `q=r_1-:r_2`	Remainder `r=r_1-q*r_2`	`s=s_1-q*s_2`	`t=t_1-q*t_2`
1		`r_1=12`	`s_1=1`	`t_1=0`
2		`r_2=11`	`s_2=0`	`t_2=1`
3	`12-:11=1`	`12-1xx11=1`	`1-1xx0=1`	`0-1xx1=-1`
4	`11-:1=11`	`11-11xx1=0`	`0-11xx1=-11`	`1-11xx-1=12`

we get answer by taking the last non-zero row for Remainder `r=1` (gcd), `s=1,t=-1`

Showing the identity, we have `12s+11t = gcd(12,11)=1`

`12(1)+11(-1)=1`