Hello! This is a good question, but the answer is not complicated.
Division is by definition operation inverse to multiplication. a/b = c by definition means that a = b*c.
Now about division by zero. a/0 = c is the same that a = 0*c. But 0*c = 0 for any c. If a isn't zero, no such c that a=0*c. If a is zero, any c suits. So for any number a the number a/0 either nonexistent or undefined (any).
Just in case prove that 0*c always =0:
0*c = (1-1)*c = 1*c - 1*c = 0
(any number may be used instead of 1; the distributive law is used).
thank you so much