We say that a R a dont equal to 0 is a zero divisor if there

\"We say that a R, a dont equal to 0, is a zero divisor if there exists b R, b dont equal to 0 such that a · b = 0.\"

I got question about the defination of zero divisor. why ab=0 since a and b both are not zero? for example:\" the rings Z/n have zero divisors for some n’s. For example 2, 3 6= 0 in Z/6 but 2 · 3 = 0 in Z/6. \" why? plz help me.