Suppose an operator types a US Bank Check Code into a machine and transposes two adjacent digits (i.e. swops the order of two adjacent digits) for example the operator types a₃a₂ instead of a₂a₃, will the machine pick up every error of this type? Does the same apply to ISBN numbers, will a machine detect transposition errors in these numbers?

US bank check codes are nine digit identification numbers a₁a₂…a₉ using the digits 0 to 9 where
7a₁ + 3a₂ + 9a₃ + 7a₄ + 3a₅ + 9a₆ + 7a₇ + 3a₈ ≡ a₉ mod 10.

ISBN Numbers have ten digits a₁…a₁₀ using the digits 0 to 9 where
10a₁+9a₂+8a₃+…+3a₈+2a₉+a₁₀ ≡ 0 \mod 11.