# Thread: question on inverse modulo m

1. ## question on inverse modulo m

Let a1 be the inverse of a(mod m) and let b1 be the inverse b(mod m). Prove that a1b1 is the inverse of ab(mod m). Thanks in advance for the help.

2. Hello,
Originally Posted by htata123
Let a1 be the inverse of a(mod m) and let b1 be the inverse b(mod m). Prove that a1b1 is the inverse of ab(mod m). Thanks in advance for the help.
a1b1ab=(a1a)x(b1b)=1x1 mod m=1 mod m, by the definition of the inverse

3. The fact the multiplication "modulo m" is commutative makes this very nearly trivial.