Exercise
The inverse of X + 1 in Q[X]/(X2)
is X - 1.
is 1 - X.
does not exist.
No, the product (X + 1)(X - 1) modulo X2 is not 1.
Yes, this is correct.
No, X + 1 does have an inverse as gcd(X+1,X2) = 1.
Exercise
The inverse of X + 1 in Q[X]/(X2)
is X - 1.
is 1 - X.
does not exist.