Yes.

Pick a pair of adjacent digits. *d* is the left one, and *e* is the right one. The multiplier for the right digit is *m*, so for the left one, it is *m* + 1.

In the original ISBN, the two digits contribute (*m* + 1)*d* + *me* to the check total. In the transposed version, they contribute (*m* + 1)*e* + *md*. Whatever the values, their difference must be equivalent modulo 11, so

(*m* + 1)*d* + *me* – ((*m* + 1)*d* + *md*) ≡ 0 (mod 11)

The left-hand side simplifies to *d* – *e*. Since *d* and *e* can range from 0 to 9 (not 10 since there can be only one 10 value), *d* – *e* ranges from –9 to 9. 0 is the only value in that range equivalent to 0 (mod 11). That value will occur only when *d* = *e*. Therefore, if different adjacent digits of a validly-formatted ISBN are transposed, they can never result in a validly-formatted ISBN.