RSA encrypt and decrypt back the plaintext, M=3, if p=7, q=13. Give necessary explanations

Hints:

C=M^e mod N; M=C^d mod N; N=p*q; e*d=1 mod (p-1)(q-1)

EXTENDED EUCLID(m,b)//finds b^-1 mod m

1. (A1,A2,A3):=(1,0,m); (B1,B2,B3):=(0,1,b);
2. if B3=0 return A3=gcd(m,b); no inverse
3. if B3=1 return B3 = gcd(m,b); B2= b^-1 mod m
4. Q=[A3/B3]
5. (T1,T2,T3):=(A1-Q*B1, A2-Q*B2, A3-Q*B3)
6. (A1,A2,A3):= (B1,B2,B3)
7. (B1,B2,B3):= (T1,T2,T3)
8. goto 2